ohboy Howdy !!!
Quick run down,,no you do not have to pay and you do not need a fishing license to fish on Disney property.
However, fishing is strictly "Catch & Release", you cannot keep the fish.
You also cannot fish from ANY dock , beach or public areas,,you can however fish from the banks (shore) along the canals, Bay Lake (the big lake) and ponds.
Disney does offer a guided Fishing Excursion on Bay Lake with fishing guide, and they provide EVERYTHING you need to fish. The guides are very good and can put you onto some real nice swimmers,,(it's pretty much bass fishing)My wife once caught a 9 pound bass on a excursion

It was sooo cool !
Now, that being said, the Fishing Excursion is very expensive, but up to 5 people can go fishing for that one price,,
if ya wanna drop a few bucks I highly recommend the Fishing Excursion, it's a blast.