Hi-
1. Yes, I would recommend that you work to transition her from needing the
pacifier to go to sleep and to stay asleep. Her ability to learn to go to sleep
on her own and to go back to sleep at night when she wakes will really only
happen once she’s no longer dependent on the pacifier to go to sleep. You can try and work on naps first, and as she gets the hang of it, remove the pacifier from her bedtime, and then move on to night wakings too. There is really no magic answer, either you can take it away all at once, or work on one thing at a time.
2. If you are doing the chair method, yes, you want to be consistent and treat middle of the night wakings the same as you do bedtime. FYI- Many times, falling alseep at night is easier to learn than those middle of the night wakings.
3. You can handle the pacifier and sleep training at the same time, or one and then the other as you suggest. it is really okay to do it however you feel the most comfortable. One one hand, doing it all at once will probably make for a quicker transition, and on the other hand, it may feel like a more gentle approach to do the pacifier then teaching her to sleep in her bed at night. The choice is yours!
And… Keep swaddling her if she seems to like it and can not get out of it!
I hope that this helps! Good luck!!!