1) Pea's limping and "back curling" are directly related, I believe. It hurts, and he doesn't want to hurt himself. If you have an injury, you aren't going to do anything to make it hurt, right? He doesn't want to either. He's telling you, "That hurts and I don't want to do it.
2) Pea's "thing" with water is quite common. Especially coming from a track, it's quite possible that he hasn't ever had exposure to this, and he thinks it's scary. He doesn't know how deep it is! He doesn't know if there's horse-eating monsters in there! You need to show him that the puddle is okay, and it's okay for him to walk through it. Make sure that when you're at the puddle and asking him to walk through it you sit up, shoulders back, seat deep, and squeeze . If he tries to go to the right, close the right "door" (using your right leg and guiding him with the left rein) and if he goes left, close the left "door," etc. Does this make sense? Make sure that your reins aren't too long. If he's a western horse, keep the reins short and make sure that you can readily and immediately direct him. If he's an english horse, make sure you have a light contact. Another important factor is that your hands are far enough up his neck – you should barely have to move to effectively make contact with him. A horse's trust in you is a faith borne not of words, but of deeds; he will begin to trust you as he learns that you will not put him in dangerous situations.
3) Pea's mysterious lameness is very serious. He really shouldn't be ridden at all. If he's had continuous lameness for 1.5 years, it is high time he gets to the vet! As soon as any lameness shows up, he needs to see the vet, really. He's not going to "work through" this limp. As soon as is possible, get him to a vet or a vet to him!
Good luck – and keep us posted!