Probably not influential as such, but in my mind one of the greats is the very recently departed Juan Nelson. Another one who caught my ear at an early age and piqued my interest in all things bass was Tiran Porter.
Don't know really. Roll a fair bit of treble off I'd guess and don't use brand new strings is where I'd start. They sound like round wounds to me but without the zingyness of a new set.
Always loved Paul Denman's sound on Sade's stuff. One of the main reasons my first decent bass was a Stingray which I still have and probably always will.