Based on personal experience, in the order asked:
1 No, just sand it to the point where the finish
is sufficiently roughed up to give the new
finish some 'tooth' to grip on.
2 Helmsman polyurethane by Minwax (Spray
cans,comes in gloss satin or flat).
3 Titebond II has helped me attach many skins to
various bows. Again, make sure the surface is
roughed enough to insure good adhesion.
There are many ways to do this, & I'm sure there'll be plenty more responses in time, but this will get you to where you want to be w/ that old friend.
Larry