1) That map seems to be accurate, but boundary lines are not real clear. In some cases property is just across the road or up a very small road. If you're in the middle of one of the obvious public areas you're probably ok.
2) more often than not, heavily posted areas are not huntable, but it never hurts to ask. After the opening weekend lots of the landowners friends and relatives have left and they are much more open to allowing other hutners.
3) Keep at it! Most of us have gone thru the struggles the first year or two of turkey hunting, but it's a sport where on the job training is the only way to learn. I know now that if I new on my first trip out what I know now, I would've had no problem taking a bird. Be patient, keep chasing. Biggest mistakes first time hunters make are underestimating how well turkeys see any movement at all, not scouting the birds well enough (sometimes it's better to just watch them one day and then hunt them the next than to go busting after them when you first see em and chasing them out of the area), not being patient to stay in area where you know there are birds and take off looking for new areas. I could probably go on and on, but just stick with it, every trip is a learning experience on turkeys-even after you've hunted them for 20 years.
Good luck!