1. Her neutral/forward throw can be cancelled into itsuuA right away then that goes into 6C, 5C OTG into your combo of choice in the air. Back throw you can do itsuuA once she puts them up in the air and it's the same thing after that.
2. That's something I'd like to know, too... I can't seem to find any good midscreen itsuuC/3C[m] combos against Carl.
3. If you know that the combo is gonna end in the corner like that, which it usually will if you're at or a little past the middle of the stage, after chun, 2c you need to do j.B j.C D airdash j.B j.C land tsubame. You have to airdash pretty close to the D, as in don't let Litchi fall down much before she dashes. You also need to stick that last j.B out kinda soon to get the spacing right for the j.C.
4. j.B is definitely a good crossup and should be abused when you get the chance. Fish for counter hits with j.C[m] and the occasional 6B[m]. I don't like using 6B because it isn't as safe as the j.C. Get those CHs and combo them into the corner and then break the seal on those foo's. The short answer is that she can be played rush down or she could be played just outside of their range throwing out pokes and looking for combo opportunities, just keep your eyes open and if you see your opponent adapting to your approach... change it up on them and do a bit more of a zone style game.
5. I try to mix it up with tsubame, airthrow~combo, and the occasional j.A spam to lock them up. Anti-airing with tsubame isn't as easy as it seemed, you really gotta get the spacing right to get it to hit on the way back down.