uh, to tell you the truth, ive never had any problems whatsoever with tapping. like, my normal setup suits it perfectly; so i really dont know what to tell you in that regard.
your tapped notes should sound at the exact same strength as your normal picked notes. its all in how solidly you tap it. like, with a good tap on and pull off. I learned to tap on an acoustic, it really helps you strengthen your tapping hand.
also, as pickups go, it depends on the sound you want. really, tapping should sound just like normal picking tone-wise. I prefer the tone of the neck pup for my solos in general, so I use that.