1. I don't think I really have a favorite issue off the top of my head, if only because I'm terrible with favorites, so in favor of that I might say her debut as Ms. Marvel in the Earth's Mightiest Heroes cartoon where she joins the team and beats Ronan. Why? Because she was awesome and she looked awesome in that episode .
Hope that's not a cop out .
2. Probably a three way tie between Kurt Busiek's Avengers run, the Brian Reed run, and the first volume of Kelly Sue Deconnick's run.
3. Eric O'Grady, if only to have her find out about him peeking on her and then see the ensuing beatdown that would likely occur .
Though more seriously, I guess maybe Sue Storm? I don't think they've ever teamed up before. I'm not sure why I'd like it so much, beyond both being blonde, beautiful, and extremely powerful women who I don't think have ever teamed up before, but I think it might be a cool team-up. A lot of the people I'd want her team-up with she's already teamed-up with, probably going to team-up with in the future, or have at least been on a team together. A team-up with Kate Bishop would probably be fun. Wasp, Miss America too.
4. Well, I'm not really knowledgeable of actors or celebrities unless they work in comic book properties, so I can't really cast anybody, but as far as who I'd like to see in her supporting cast? Well...I think it would be cool if Carol has a dual Earth/Cosmic supporting cast, and as far as the Earth supporting cast is concerned I'd probably include Tracy, Wendy, Kit, and Chewie (even if Chewie fits under Cosmic as well). For Cosmic, if Mar-Vell ends up being involved in the films and dies, I think it would be interesting to see Carol interact with his children, Genis and Phyla, and give both some due in the movies.
With their relationship with Sony as it is now, I think Marvel could probably do something with Spider-Woman in the movies now without too much trouble, and introduce Jessica to the MCU. If they don't want to give Jessica her own movie, why not integrate her into the the cast of Captain Marvel as Carol's best friend who's semi-retired from the Superhero or spy game like she is in her current book? That way, Carol at least gets to keep one of her best friends named Jessica!
I don't really have strong feelings for the Rhodey relationship, but considering we're probably not getting an Iron Man movie in the near future nor a Rhodey solo, maybe War Machine could be reincorporated into Captain Marvel's supporting cast?
Be also cool to see Monica in a Captain Marvel movie in some form as well.
5. Man, Gail Somone from Holt was an inspired choice, but if I had to pick someone who hasn't written her yet? I don't think Kathryn Immonen has written her in a significant way so that would be cool, as would Aleah Baker or Kate Perkins. For guys, I don't think Greg Rucka has done anything with her so he'd be awesome, as would Jeff Parker or Grant Morrison.
6. I knew about her from X-Men: TAS way back when thanks to the episode that dealt with her connection to Rogue, but it was EMH that made me a big fan of her.
7. Chewie is really cute.
8. The Juggernaut.
9. Pre-last mindwipe: Spider-Woman, Vision, Scarlet Witch, Wonder Man, Spider-Girl (Anya), 3D-Man, Rogue.
Post-last mindwipe: Spider-Woman, War Machine/Iron Patriot, Agent Venom, Ms. Marvel, Blue Marvel, Miss America, Black Panther.