Are there any parks allowing dogs playing and running loose? I mean, dog parks. In West Georgia?

Yes there is

Yes, at Longview park in Carrollton. It is behind tennis courts. I take my dogs to Little Tallapoosa park on hwy 113 just outside carrllton, and they run on trails,river and large field. I have let them off leash but they wear a shock collar. Some people have had their dogs attacked by other dogs and needed surgery @ Longview dog park. My dogs don't get much exercise here, they just run around sniffing poo.

Yes, on Longview in Carrollton