Please don't take him back to that store! He is very skinny, he has lots of bites from tank mates he shouldn't be housed with, and yes it looks like severe tail rot. I see a bowel movement in his tank so that kind of eliminates impaction, which often causes paralysis of the back legs. We may be able to help you, but we really need you to answer the questions about your set-up as far as what exact lights you have, the temperature in his cool side, hot side, and basking spot, what his diet has been, etc. He obviously was dominated by tank mates and didn't get much to eat, and they would have eventually killed him judging from the bites all over him and the tail rot. If you take him back he will surely die...
Please list all of your setup details and answer the questions, and post a photo of the setup. If we can make sure your setup is correct right off the bat and that he has the correct lighting and temperatures, he can recover...You just got him so it's not at all unusual that he isn't eating yet, that's simply relocation stress, so don't worry so much about that. He will start eating soon as long as you have adequate UVB lighting and temperatures. He's active, he's moving around well, he's bright, so the not eating a few days after he was brought home is normal. He's got a very good chance of living a healthy life and recovering, but you need to be patient and help us help you. He won't recover over night, but he's not lethargic and he seems very alert, so if you keep him that way he should start eating soon and with proper husbandry he should recover. If you take him back to that awful store he's dead for sure.