I'm not sure about fishing or launching in the Everglades National Park, however you can launch at the Loxahochie Reservoir ramp which will lead you right into the Everglades. Loxahochie is like the head waters of the begining of the "glades". Free to launch the last time I was there. Lots of nice bass to be caught in there. Also lots of nice gators too!
you can access the glades at holiday park at the end of griffin rd in dania (ft lauderdale)-they rent boats and there is a ramp for launching your own--bait and tackle shop, cold drinks, convenience store, air boat rides etc-don't know what the fees are if any-
griffin rd can be accessed off i95 and university dr just to mention a few-