IMO, the reasons why horses misbehave is either lack of/bad training, pain, or fear.
It sounds to me, with what you have described, that your guy may be in pain. Do you have any idea of his training level? I know you haven't had him for very long, but if he was trained well, and knows how to correctly walk, trot, and canter, I would say he is in pain (more than just tight muscles).
**What is your level of training? Have you had/do you have a trainer? When you ask him to turn, what cues are you giving him? Do you ask for the turn with your leg first? Do you support the forward momentum by reinforcing the forward momentum with your inside leg?
He can't trot or canter a circle becasue he is very tight in his hamstrings so he can't carry himself properly.
Is he lame? Maybe he's more than just a little tight in his hamstrings?? (I hope not, but it could very well be the case)
When I use the reins to stop him galloping off, her sticks his head really high with his nose sticking out, what can I do to help him?
There are different things you can try for this, but I would first make sure he's not in pain elsewhere. You could try a different kind of bit (for example if you're using a snaffle, you could try using a Waterford or something without the hinge in the middle)
I don't like hauling on his face all the time, if I loosen the reins and turn him in a tight circle everytime he rushes off, he slips over and falls to the ground,
Again, it sounds like he's in pain. I would take him into a round pen and see how he moves there. If he limps on any of his legs, I would call a vet to check him out.
If he is sound, I would try a different bit, but would also do a LOT of ground work, a lot of work in the round pen, etc. to build a base of trust between the two of you and let him work on his balance.
Hope this helps, and keep us updated!