@Deikard:
1.) After PO A, the attack you do to follow up really depends on the situation. It's very hard to gauge your options online where latency ruins Taki... First of all, you have to confirm whether PO A hit or not. If it's blocked, there's little you can do in terms of a followup attack... but if you master your move properties, you can perform moves in anticipation of your opponents' responses. For example, 22A is a tech crouching move with a built-in step. It will duck highs (like throws) and sidestep a good deal of verticals. That being said, attacking after a blocked PO A is generally not the best way to go, gauge your options and go from there. After PO A connects though, that's a whole different story. Your standing A will interrupt any non tech crouch move they throw out, so you can just go back and do AB -> [whatever you want] and go from there.
2.) Attack strings, like flowcharts, really depend on situations occurring within the strings. Was your move blocked? Did it connect? etc... I believe, though, that Taki's core gameplay relies heavily on her AB and its various followups. A simple string to stick to (and really, what you should be using instead of BA) is AB214(PO)>PO A_K_B. Now... If AB connects, PO B is a good choice as it will interrupt a lot of retaliatory moves and is one of her more damaging PO moves. It's also safe on block and does good soul damage. If AB is blocked, PO A will still interrupt a lot of moves, given they're not tech crouch like Siegfried's 3B. PO K may also be a good choice if you anticipate them just standing there blocking as it will give you advantage on block. Be aware though, that both PO K and PO A are high and really duckable. Check out the various threads here to bolster your attacks. (I highly suggest reading the stickies). Also, expose yourself to competition, it's really the only way to pick up and modify strings.
3.) This is a matter of preference. So I have no real answer to that. I use a Hori stick... But if I'm forced to use a pad, I assign A and B on individual shoulder buttons. A+K would then be a shoulder button + a face button. I know that's weird... You might as well assign A+K to a shoulder button... Far as I can tell, there's nothing stopping you from doing that.