Ok the thing with their names of the moves, what you said they are, is what the moves are, just in Japanese converted into Romanji.
Now for your questions:
1) double tapping back is indeed a backdash, however some characters have advanced movement options like Lady Kstoute and Momiji and Misty and Ayane, they all have back flips.
Ayane has a an advanced shuffle called the hajin back dash, Misty has a forward dash that can be cancled into a throw, a critical burst or a up kick. Now Momiji has the back flip and Tenku which is a forward flip that can lead into a ground slam with punch a knock back kick and a throw it's great for mixups. Phase 4 has teleports where she like Momiji's tenku they end in punch, kick or throw, those are all chinfu. Lady Kstout'es back flip can be turned into a charge that can splat people from range it's very useful if you can catch somebody off guard, if they block or hold, well you in trouble.
2) Back flips are good for space then they also have advanced forward dashes with fly with Lady Kstoute. Momiji has Tenku that can also be charged as an air dash which can end in a power blow. She is a jet plane which is awesome.
3) Walk speed is about the same with their attack speed of course Ayane,Misty and Christie are the fastest but remember some attacks can better slow the pace of you trying to move up, better to dash if you can. For Poke, bait and punish, Lady Kstoute is more for that due to her slower moves and tricky movement, so is Momiji with the range on her best attacks and her safety, Ayane is all about whiff punishing because she has moves that crush and those lead into launchers and her damaging combos, she also has great throws. Momiji and Lady Kstoute also have great throws too, and with a great throw punish you can set them up pretty well since either it puts them back, or in the air for you to follow up or straight on their faces. Ayane too can do that and she gets deadlier with a wall with you.