Akuma - Select E Honda, then hit up and you can select Akuma. Playable everywhere. You might get frowny faces from regulars since he is normally banned.
Classic mode is the original Super Turbo game, unchanged. HD Remix adds changes to the game, like making certain moves easier to pull off (like Zangief’s SPD no longer requiring a 360 motion). The thought was that the changes would make HD Remix more balanced than Classic, so that certain characters would have a fighting chance in matchups where before they would get dominated for free.
Characters can do wakeup moves, so I would assume yes she can get thrust kick out on wakeup if timed right
Akuma is above Honda. You can’t see him on the select screen, but he’s there. He’s a pretty broken character, even after he was “toned down” in HDR, so it’s not a good look to use him online. He is banned at tournaments.
In Classic mode, you can play as the “old” versions of all characters by inputting a special code. The same goes for selecting Akuma, but the code is much more complex.
HDR Remix essentially applied a series of changes to Super Turbo. Classic mode is the original ST.
Yes, she can do all of her specials on wake-up. The reversal timing in HDR is extremely strict compared to modern games. You essentially have 1-frame to get a reversal.