Pretty good analysis, except that:

@10 there is contact:

See Case 144.  Since 10 did not need to tack to ROUND the mark, but instead chose to tack after rounding Rule 18 does not apply and regular Part 2 Rules do.  Rule 13, while tacking or Rule 10 Port Starboard 

Let me try this line of thought:
General consideration: as tacking is initiated a boat is swinging rapidly from one tack to the other.  
Yellow is going through this motion starting at position 8 and ending shortly after position 10.
Conclusions:
At position 9 yellow passes htw an d is keeping clear given that blue, on her course at position 9, will pass astern of yellow.
At position 9, Blue is now ROW boat and changes course without giving yellow room to keep clear.
Yellow is compelled to breaks 13 as a consequence of blue breaking 16.1
Blue obtained an inside overlap between position 7 and 8.  
Since then yellow was either mark room boat or was unable to give mark room to blue; therefore she was not required to do so under 18.2 (f)
It is clear that yellow is tacking; therefore blue needs to act to avoid contact which she does not thus breaking 14. 
Decision:
Yellow is exonerated under 43.1 (a)
Blue is DSQ for breaking 16.1 and 14 

I think you are misinterpreting Mark Room Specifically: mark-room for a boat does not include room to tack unless she is overlapped inside and to windward of the boat required to give mark-room and she would be fetching the mark after her tack.  There is no mark room relationship between Blue and Yellow at 9 or 10 on the diagram.  Room in this case as defined by the definition Room,

From 9-10 Yellow is Tacking under Rule 13 and MUST keep clear (has no rights) After 10 she is a Port Tack Boat and Blue is on Starboard.  I don't see any case where Yellow is ROW here.

An alternate scenario would be Blue preventing Yellow from coming up to close hauled on Starboard (no tack involved), in which case yes that would be a problem.  Rule 18 does not apply though.

As for the Rule 13 situation, Yellow is Tacking  (which is also changing course). She is tacking into a give way position and sailing above proper course. Blue is changing course yes, but only to come up to proper course on Starboard.  As clear ahead boat, Yellow can luff, and Blue would have to respond.  However as soon as Yellow Begins to Tack, Rule 13 applies which precedes 16. She is clearly the give way boat and changing course. Blue is not required to anticipate Yellow braking Rule 13 and would be exonerated if the collision was minor. 

A similar case: RRS | USA Appeal US89 (racingrulesofsailing.org)

Hi John,

1. Mmmm! Pedantic! But if you look closely at the drawing, you'll see that at P9, Yellow is beyond htw by at least 2 picometres! ;)
2. In the situation I encounter, after the last Mark, it is sometimes possible to lay the finishing Mark, or there is slight wind shifts so that port is the best tack to leave the last Mark - but many skippers either miss this advantage, have boat which doesn't point so well, or simply prefer to tack after holding a few boat lengths on starboard (I've added a clarification in italics to the question). Therefore, in my scenario, it is not really Proper Course to tack at the Mark. Nonetheless, thanks for your assessment if it really is Proper Course for Blue to tack. I hadn't considered that. If there isn't Mark Room for Blue, then I think our assessments are the same (though you've added some detail with respect to damage - a rarety in RC racing)

Hi Marinino,

You've said it the way I see it - except that you've pointed out 18.2(f). I hadn't thought about that. R18.2(f) probably kills the claim that Yellow failed to give Mark Room (based on the scenario in which Proper Course does not require a tack). But I still wonder if Blue can claim exoneration because she was nonetheless sailing within Mark room to which she is entitled, therefore avoiding disqualification R43.1(b) " When a boat is sailing within the room or mark-room to which she is entitled and, as a consequence of an incident with a boat required to give her that room or mark-room she breaks a rule of Section A of Part 2, rule 15, 16, or 31, she is exonerated for her breach.".
Thanks

Sorry somewhere there is a case that is exactly this and I was frustrated I can't find it! I just kept commenting as I searched. But anyway I'd treat is as if someone crash tacked in front in open water.  Rule 13 gives no exception other than for simultaneous tacks so it is incumbent on you to make sure no one will be in the water your tacking into. Yellow was right of way, but changed course to head up (Rule 16) and then started to tack (Rule 13) Blue should be luffing up as fast as she can in response to keep clear, (she is not entitled to mark room so there's no defense about being forced into the mark)  but could also argue she was preparing to duck, since how to keep clear is her option).  Once Yellow tacks back towards Blue however, she probably can't keep clear without anticipating yellow would break Rule 13. The damage bit has to do with Rule 14, the Right of way boat can only be exonerated if there is no damage or injury. Not sure how that translates to the RC world... 

Hi Craig,

I don't think your first Case 144 is the same situation.
I haven't claimed that Yellow has right to tack because of Mark Room. Simply that she is not breaking R13 because Blue was not on collision course at the time - and Blue (ROW) is limited by R16.1.
There is an arguement that at P9-10, Blue is inside boat and has Mark Room (R18.2(a)). (though there is also an arguement that Blue does not have Mark Room!)
 "Yellow is Tacking  (which is also changing course)" - but as Keep Clear she is not limited by R16.1. Furthermore, R16.1 applies to Blue (ROW), even if the change of course is to round the Mark.
US89 - this doesn't seem the same scenario. There is no denying that Yellow (in my scenario) looses Mark Room when she tacks, nor that she doesn't become Keep Clear - the point is that Blue is "Limited" by Section B, Part 2 rules.
Unless I'm missing something here?
Thanks for comments.  (Comment added before reading Craig's last comment)

Stewart
You are correct: most likely 43.1(b) provides exoneration for 16.1 
I have no factual information on the absence of damage so I did not include 43.1(c) providing exoneration for 14.
For boats bigger than RC ones, the dynamic of the incident could most likely result in some damage ...

Stewart Campbel
said Created: Today 16:04

 
I'm a simple soul.  Your OP said "at P9, Yellow is htw".

This is a rules discussion.  You're meant to be pedantic.

But I agree that nothing is happening @9 or @9+delta, so it doesn't matter

Hey, you've shifted the goal posts (or rather the mark).  Did you fly flag C with repeated sounds and display a green triangle?

If it's not necessarily the proper course to tack at the mark, then rule 18.1 last sentence won't apply.

I agree that Marino's use of rule 18.2(f) is inviting.

Craig appears to be saying that at some point, mark-room has been given, so rule 18 is off and doesn't even apply to Blue.  I need to have a good think about that, in particular which bits of mark-room may or may not have been given.

I've been having a think about Criag's contention that from the time Ypasses head to wind, rule 18 does not apply at all to either boat.

I agree with Craig.

Here's my logic.

Assume Y claims that her proper course is on port tack and Y passes head to wind @9.

@8, Y's proper course is to sail close to the mark, and her mark-room entitlement includes room to sail to the mark, and B is giving her that mark-room

@9-delta, immediately before Y passes htw, her course is still to sail close to the mark, her mark-room entitlement is still to sail to the mark, and B is still giving her that mark-room

@9, Y having passed head to wind is no longer entitled to mark-room (rule 18.2(d), at least, no matter what other rule may apply), whatever her proper course she is not entitled to any mark-room.

So, up until Y gave up her mark-room by tacking, B was giving her mark-room.

So, by common english, Y has been given mark-room, and then, by rule 18.1 last sentence, rule 18 no longer applies between Y and B, so B is not entitled to mark-room as inside overlapped boat.

Ahh! So the 2021-24 version of the Rules has the additional statement in R18.1 that "Rule 18 no longer applies between boats when mark-room has been given".  That sounds like there can only be 1 round of "Mark Room" between boats. If this is a correct interpretation, then in the described incident, Blue cannot have gained Mark Room (because there has already been one round of Mark Room between Blue and Yellow) so Blue cannot be exonerated?

So, taking account of all the comments, my original new take would become :-

"My take is at P8, Yellow is ROW (R11/R12) and has Mark Room (R18.2(b)). Immediately after P9 , Yellow looses ROW and looses Mark Room. Immediately after P9, Blue Gains ROW (R13) and (maybe?) Mark Room (R18.2(a)). Blue is NOT entitled to Mark Room because R18.1 last sentence and 18.2(f).  Blue, with newly attained ROW continues to change course round the Mark and infringes R16.1. But since she does not have also has  Mark Room  (maybe?), may be she is not exonerated?.  Is  Yellow, having been hit while Blue infringed R16.1, and   herself having infringed R13, is entitled to exoneration?. Neither boat is expected to anticipate the other's actions. R15 doesn't seem to apply since Blue gained ROW through the actions of Yellow.  Addendum - Immediately after P9 boats are on opposite tacks and if B's proper course at the mark is to tack, then rule 18.1(b) applies to switch off rule 18 in its entirety "

Re-written neatly :-

My take is at P8, Yellow is ROW (R11/R12) and has Mark Room (R18.2(b)). Immediately after P9 , Yellow looses ROW and looses Mark Room. Immediately after P9, Blue Gains ROW (R13) . Blue is NOT entitled to Mark Room because R18.1 last sentence and 18.2(f).  Blue, with newly attained ROW continues to change course round the Mark and infringes R16.1. But since she does not have Mark Room she is not exonerated.  Yellow, having been hit while Blue infringed R16.1,  herself having infringed R13, is entitled to exoneration. Neither boat is expected to anticipate the other's actions. R15 doesn't apply since Blue gained ROW through the actions of Yellow.  Addendum - Immediately after P9 boats are on opposite tacks and if B's proper course at the mark is to tack, then rule 18.1(b) applies to switch off rule 18 in its entirety

Have I got it right now? (or is there more!!?)

Thanks for all comments.  

Seems that everyone is over complicating the issue, which is quite common to both Team Racing, where the first mark is left to starboard and in Match Racing while boats are circling pre start. Rule 18 ceases to have any relevance once the yellow boat passes head to wind. 
At position 9 if blue holds her course she will pass astern of yellow. Yellow does not need to anticipate that blue will alter course - I see no reference to "proper course" in 16.1. Blue is obligated by 16.1, if she alters course she has to give yellow room to keep clear. If she establishes a collision course then yellows options to keep clear are very limited, if she luffs her stern will swing towards blues bow, and the impact will be greater. bearing away may delay the impact but will not enable her to keep clear.
Blue may be able to give yellow room by continuing her turn, if she goes through head to wind they may be subject to rule 13 at the same time as yellow, in which case yellow remains the keep clear boat, but it is possible that yellow will have completed her tack and it will be blue that is subject to rule 13.
At some stage they will both be on port tack and yellow will be the windward boat, so we could be looking at a couple of instances of rule 15 applying.
Experienced team racers faced with this situation generally luff head to wind and force the following boat astern of them, since they retain their rule 18 rights in this way. Inexperienced team racers coming into the mark late luff in an attempt to catch a boat which has tacked onto port, for a starboard rounding, and are surprised to be penalised under 16.1. 
43.1(a) gives exoneration to yellow - it was blue's breaking of 16.1 which may have caused yellow to infringe 13 or 11.
Not the sort of scenario you want to take into the protest room and the reason Team Racing and Match racing use Umpires.  

Hi Nigel,

I don't think everyone is over complicating the issue.  I think you have simply stated my own summary, which was based on the comments (but you have extrapolated and varied some scenario). The discussion has centred around whether Blue might obtain Mark Room. Sure, after introducing and evaluating some R18 details, the conclusion reached is that Blue does not obtain Mark Room. Perhaps you have already been down this route of analysis and can confidently state "Rule 18 ceases to have any relevance once the yellow boat passes head to wind". But for my part, I am grateful for the discussion and the conclusion (that Blue does not obtain Mark Room) - most especially that the conclusion has been reached after analysis of the rule (R18). I am now comfortable to defend the prompt tack at the Mark and now can quote the rules which deny Blue Mark Room.

Thank you for your comments, and for discussing some of the alternatives which might occur.

Stuart,
Did RC refer to Radio Controlled racing? 
If so, you have my deepest sympathy and best wishes, as events happen so rapidly and angles are so difficult to judge that I am in awe of how anyone resolves rules incidents. But at least you probably stay dry while doing it! Enjoy.

Hi Nigle, (sorry, "Nigel")

Yes, RC = Radio Controlled. I used to be a wizard university team racing (dinghies) in my youth. But at 73, RC gives all the thrills of the race without the discomfort. We get in 12 races an afternoon so maybe 72 mark roundings. And yes, it can be difficult to see and resolve incidents. But incidents very rarely result in damage - too much wind for too big a rig does all the damage. And of course, replacing a damaged sail costs a few tens of GBP/AUD rather than thousands. And after a day's racing, just pack the boat in the car and drive home. No expensive mooring or storage charges. Leaves more time (and money!) for the motorbike and bicycle!

Chookas, Stewart

Nigel, please come and join us some time. RC umpiring is fascinating. We work with an observer, who is also a competitor in the event. They provide input in to what is happening and the umpires can then apply the rules.
We have a set of rules for umpired racing, a Call Book, and often use an accelerated protest procedure, much inspired by what happens in team racing.

Gordon