PHP is going to be an absolute must for what you want to do. As far as where to host it, I've seen PHP hosts, but I'd strongly advice avoiding them. You are much better off just finding a webhost. If your needs are small, finding a free webhost should do just find, as long as you don't attract too much attention from the host. (They are known to randomly delete stuff).
The main issue is that you couldn't integrate it with the user account used on the forum, since forumotion doesn't give database access. If you are creative, you can still make it feel integrated without it, but it does add the extra barrier involved. It's all about what your members want and expect for the whole experience.
As far as hiding information from the public, while still having those fields, that's simple PHP. If you can get a place to host your gallery, and the integration isn't a problem, programming it the way you want it shouldn't be too hard