Yes, they can be reversed. My husband had the reversal procedure and now has a completely normal sperm count. After all of that, it turned out to be an issue with me and we still ended up doing IVF.
There is another option where they can retrieve the spem from the man via some type of needle aspiration I believe. Sorry, I can't remember the name of the procedure, but your RE should be aware of it.
Yes, but depending on the length of time between the vasectomy and reversal it may cause some problems with conceiving. My husband had a vasectomy almost five years ago and the 2 urologists we saw suggested IVF with ICSI rather than a reversal. The reversal can cost as much as the IVF procedure. We decided to try IVF with ICSI rather than the reversal, however, if I had the choice again, I would chose the reversal first. Good luck, let me know if you have specific questions since we recently went through it.
Yes, there are surgeons who can reconnect the tubes. Good luck!