For the questions posed above, I believe 2 weeks is the maximum limit for state parks, but you'll have trouble staying 2 weeks straight at any park at this point in time. (I got one place for 2 weeks, but I'll be in 3 different spots.)
If you get to Florida on the I-95, make sure you stop at the Welcome Center and get a map (and any info) of the state parks. I was able to get sites in several parks along the east coast, then over to Highlands Hammock in the central part, then up to Lake Louisa, O'Leno, Suwannee River, Henderson and Topsail in the Panhandle.
Perhaps I'll add that I'm trying Florida again, but I've been in Arizona for the last 3 winters and have enjoyed it very much. Happy trails.