Not an easy answer.
1. do realize that with 1 midi pickup, you only midify the melody strings. If you choose to midiy the bass strings also, keep in mind that the lowest strings have so much tracking delay that you’d probably will have to do some editing afterwards. Tracking of the melody strings on a Stick is excellent, by the way (far better than guitar).
2. If you would want to write the stuff out in standard notation, than Logic is really good for a special reason: Logic has thing called “environment”, which is a kind of programmable midi router. I made a special environment in Logic that can tune the pitches of the melody strings to those of the bass strings. That way I can record the bass part in one take, and the melody (without “retuning”) in another take.
3. sorry, no idea if there’s any automatic TAB creation program. I made such a program on my old Atari computer (Atari was very easy to program midi stuff on). Because I played each string on a different midi channel, the TAB program knew what note was on what string. Most notation programs can’t do that (shame!).