I know that you are dealing with a lesson horse, and as such he might not be very responsive. Probaby has a mouth of steel.
Here's my thoughts on the halt and on him walking off.
At the halt, like when you are waiting for your turn in the group lesson, give him so much rein that there is some loop in it, so there is NO pull on his mouth. HOWEVER, put your hands on his wither (in fists , 'cause you're holding the rein tightly) on each side of the wither . If the horse barges down to try and rip the rein out of your hand, you will have such a firm grip that he will hit the bit and decide to "bounce" off of that bit and come back to where the rein is loose. Just be sure that he does have plenty of loose as long as he keeps his head in a natural, relaxed position, but is NOT barging down (pigrooting).
If the horse starts to walk off toward the others who are in the middle of the arena, you take up one rein and turn him in a very tight circle a couple of times, then let him out when he is facing the way you want him to be. Again, you have to be able to lengthen and shorten your reins, quickly and adroitly. YOu can actually practice holding reins when off horse. Get yourself a practice pair, tie to a chair and pretend away!
I know you are in group lessons and read your other thread about wanting to start dressage soon. I think that spending some more time learning to be ok on the back of the horse, and deal with some of these less fun issues will untilmately make you a stronger, better rider.