Sorry, I forgot to post my own opinions:
1.) Lose, unfortunately. Mara is a trained assassin with incredible skills, both the traditional Jedi set (saber dueling and Force powers), but also the more shadowy areas of combat and killing. Barriss wouldn't stand a chance.
2.) Lose. Not even a contest.
3.) Win, but barely. Barriss has worked with Anakin before and knows a good deal about his strengths and weaknesses. In addition, Anakin was a bit of a berserker right after his fall, and I think her own caution and strength would have brought him down eventually.
4.) Lose. Dooku, being one of the best duelists ever, and not too bad in the Force department either, would absolutely crush Barriss.
5.) Actually, I don't know much about Darth Bane's powers myself. I'll leave that to someone else to decide.
6.) Lose, without a doubt. Maul was a brute, and he was incredibly fast and powerful with that double-blade of his.
7.) Win, actually. Kas'im was very skilled in lightsaber combat, but he was arrogant. She would have had a tough time of it, but she would have pwned him in the end.
8.) Win. Unlike Kas'im, the Jedi weapons master wasn't (too) proud and arrogant, and Barriss would have had a much harder time of it. However, she demonstrated that she had an incredible degree of Force control in TAS, which the old man didn't.
9.) Lose. Do I even have to give my reasons?
10.) Win. Although some might disagree, I say that Luminara got to be too set in her ways. Barriss eventually outshone her old master, although their partnership was very much an Anakin-ObiWan kind of thing. Their styles were very similar, but I think Barriss would have destroyed her in both arenas.
Okay ... now what does everybody else think?