Anything that's not Story or Training will let you unlock titles.
They're not. I flip flopped sides a few times but she only has one and it's still 1H for both. Watch again and you'll see what I mean. The game shows you every counter you can do in Command Training.
She LOOKS very cool. She's pretty awful, though. To test, I ran her against Rikuto when he was over for games earlier. I won the very first match we fought, then proceeded to lose about 21 more in a row before taking a second. She has no wake up kick and if she's against a wall she's completely dead since you can't get people away from her. She's all shenanigans and while she's completely fun to use when your friends have no idea what she's doing, give them about five to ten matches and they'll start smacking you around if they're even passable at the game. Once you get over the fear of what she can do, you realize she really can't do much at all and just rush her down.