Is there anything I have to do to keep my horse's teeth healthy. Do they need to be brushed or certain things given to them to keep them in good shape? Do they even make toothbrushes big enough for a horse?

Horse's teeth continue growing throughout their lives, constantly being worn down and replaced. There's not that much you need to do to keep their teeth healthy other than to make sure that they are being worn down evenly and there are no sores inside the mouth.

How often is it needed to check their teeth in case they get worn? It is something that can be almost predicted like maybe every 6 months they need a good full check?

I think you can get a farrier or vet to open their mouth and look when they get a regular checkup. Teeth only grow slowly, so it's not as though it's something that will happen overnight.