Seaplanes and Seaplane Tenders

Following a previously successful discussion on WW2 naval aviation yesterday, I've encountered another hitch in my reading.

What exactly was the function of a "Seaplane Tender" as used by the IJN and USN? By the size of the tenders themselves they don't look large enough to carry a very large compliment of seaplanes. We're they just for resupply and refueling? If not, how did they manage to carry a worthwhile number of planes?

How did seaplanes make it to the actual AO of a battle? We're they hauled, or did they fly out and refuel on site?

What advantage would a seaplane actually have over a conventional aircraft? I'd imagine that they would save on limited carrier runway space, but did the planes themselves have any other advantages?

Thanks!