I would imagine it has an impact, particularly if it is way off centre, probably affects your tone as the magnetic strength would vary and the vibration of the string would be slightly different than if it were aligned to perfect centre. Maybe someone on the forum can give you a more scientific answer.

Depends how far off ? Usually has a SLIGHT effect on bending..

I've noticed that with a certain setting on my 60's fuzz (maybe affecting compression??) when I bend a mid-neck note on my Squier's neck pickup, there is a serious drop and swell in volume.. Otherwise in my experience, its all very slight, as MikeM says.