Anchor the vanity, then the top. The backsplash probably would cover any small gaps between the top and the wall. It would look best if the top was flush with the wall at the ends if you can do it. If the wall is bowed, that may not be possible. Same thing with the backsplash...granite won't bend to fit an uneven wall, but small gaps can be filled with caulk.
I use a 100% silicon adhesive/caulk to attach the couple of slabs I have to the counter as well as the backsplashes. You can use a razor blade to clean off the squeeze out at the junction leaving an invisible joint - and use an alcohol wetted finger on any areas that may need a bead. If your wall is straight, you may not need any visible caulk at the top.
Not all stone labeled granite really is, and some silicon can stain some stone. The stuff I have in my home hasn't been a problem. If you had this fabricated rather than buying a prefabed piece, check with the fabricator for their recommendation as to what to use.