Many of the WMA's (Wildlife Management Areas) have a stand-alone small game hunting season, usually later in the year... in my opinion, that would be the best time to plan on "hunting and moving" as yes, you will most likely annoy deer/hog hunters perched in a tree when you walk by.
For squirrel, just look for a food source such as acorns. Walk in before daylight, take a seat, and if there are squirrels around you will see them in short order IF you stay still. If after about 30 minutes you don't see some, walk a quarter mile and repeat. Usually the first couple hours in the am are good and the last few hours of the day are good. Squirrels will "bark" at you and it's their way of sounding an alarm... just hold still and sometimes they will come closer for a look.
In cooler weather, it's fine to clean game once home... if warm or hot, best to clean ASAP and get the meat on ice.
If it's warmer than 60 degrees, you will most certainly want to invest in a couple ThermaCells so mosquitoes don't kill you.
Where in FL do you plan to hunt?