Frist of all has she been spayed, in regards to taking her to the dog park, any dog of same sex that has not been fixed, will be very territorial, the dogs at the park trust me are not all fix, so just be on your toes, and keep your leash on you just in case you need to loop her neck quickly to break up the fight, which can happen in a quick second. You still need to be always on your toes when taking any pit for socializing especailly to a dog park, they are just like humans they have bad days too, and there are some dogs LOL that can be getting on its last nerve as well. You might want to take a obeniece training class, great way of socialization for pits. Keep doing the daily walks, taking her to the pet store, car rides. Also invite one of your friends over that has a dog to your home. Its a slowly way of socializing.
In regards to the seperation anxiety, try the thunder shirt, that seems to help alot.
The territoral thing alerting everyone that walks near the home, she is doing what she was breed to do. Protecting her family/belongings. I wouldnt take it to heart.