yes, virginia
First of all, I do not want you to feel at all pressured. I am really laid back about the whole thing, and frankly you've already got points just for volunteering for even one of these fandoms.
In general, I like clean, intelligent writing. I also like references and allusions to other things. (You do not have to be as in-jokey as T.S. Eliot or anything. I'm just putting that out there. If you want to reference The Republic and Crime and Punishment in fic for Lawrence of Arabia then please knock yourself out.) Plot is lovely, but far from necessary. I would rather read about character. Plot as a key to character? That is great. I am not so crazy about flashbacks, but only because people tend to do them poorly. Obviously, if you feel a flashback is needed then you should RUN wit that.
Um, my only Big Squick is incest - this squicks me no end - but I think in general my tastes are pretty vanilla. I am a fan of slash, but sometimes I am even more a fan of unrequited sexual tension or homoeroticism or even just heterosexual life partner-ism. Tension > resolution, imo. (But I also do love reading about resolution...I just feel less high-minded.)
I dunno. Use your common sense.
Some specific notes:
For Lawrence of Arabia - like everyone else, I am a big fan of the Lawrence/Ali relationship, so I would love anything that explored that. (Especially Ali after the war.) However, I would also happily read about Feisal, or Allenby, or Dryden (I love me some Claude Rains), or Auda...you see. WWI is fascinating! I love it all.
For The Sun Sword - you are insane for offering to write in this fandom (if you did). I salute you. Anyway, who do I like? Everybody. Avandar and Jewel are my favorites, because I find their relationship and the power dynamics really interesting. Also, Avandar is hot. But I am also a fan of Teresa, Kallandras (and not just because he has sexual chemistry with everyone he comes across), Diora, Valedan, Kiriel, the Ospreys, Celleriant, Amarais, Evayne, the Voyani...you get the picture. If they are in the books, then I will happily read about them.
Emer is my favorite part of Celtic Mythology, and I know that is kind of weird. If you could work her in, on her own or with other characters, I'd be forever greatful. I'd also happily read anything about Cuchulainn's relationship with Ferdiad (and for the record, foster brothers having sex does not equal incest). But really, I'd be happy for anything involving all three of them. I have a thing for people who love each other hurting each other beyond repair.
Lastly, Patricia McKillip's Riddle of Stars books. As I said in the request, I'd love anything about Mathom's family because they are my favorite. However, I'd also love Raederle and Morgon, or El and Deth, or any of the characters singly. Or Tristan and Eliard dealing with Morgon, or having Raederle to dinner! Or something. Or Har and Suth. If you can capture any of McKillip's world, then I will be very impressed and extremely happy.
Thank you so much for doing this, Yuletide Santa! I'm very excited to read what you write.