Duno about ponies but horses i reckon its approx 6 or 7 , i bought 2 16.1 hh horses aged 5 who have both ended up being 16.3 hh and i am just a short arse at 5'3''.
I twill depend on the breed and the type. I had several New Forest ponies in the past and although some of them were quite large and I was worried they would go over 14.2 they never did - it's in the genes. I would say they make their height about 6. Of course, if they are Welsh I think you can re-register them if they go over. Dartmoors etc. are normally quite dependable if you know the size of the parents. Welsh Ds can get huge (again) talk to the breeder, they'll know the lines. Does this help?
It depends on the pony I think, but I would have thought by 7 they should be just about finished. I bought a 5 year old forester who grew over 2 inches in 15 months. (That was good actually, he was 13.3 when we got him!) Our other forester didn't grow any taller, but has filled out a lot.