I just had mine removed like 3 months ago. I'll answer your questions in order.
I asked my doctor about it and he recommended me some in network surgeons, so finding a place to do it was easy.
For recovery I remember laying in bed for like 4 days before I got a bit more active. I could manage pain just fine with otc meds. A lot of my pain I think was nerve pain, which I felt moreso in my inner upper thighs rather than my groin and I found that using an ice pack helped a lot. I felt a lot better after just one week, but I did still have to take it easy with activity for about 6 to 8 weeks.
I do have extra skin. If you want to get a vaginoplasty in the future, you should leave it since they will use that skin. I imagine that you could get it removed if you want though.
Mine was around $24,000 without insurance. I'm on my parents insurance still, and my Mom had a surgery that maxed it out, so I was very fortunately fully covered and paid nothing. The surgery itself was $20,000 but then you have things like anesthesia, getting the letters, the consult, and pre and post op appointments.
After the procedure they gave me pain meds and a laxative. Didn't really need the pain meds and I used the laxative for like a week. I also have stopped my T blocker since, which is nice.