Some, not all can still get it "up", but it is not as full. Getting a rise is a mental thing. You can even have sort of an orgasm, nothing like a current one though and to get there takes A LOT of work from what I have heard. If you do not "exercise it", it will shrink, which could effect things later possibly.
No, they will not pay for it unless it is required.
The military does physicals. I know they did one on me at the 2 year mark and when I got out. The old turn your head and cough is going to be pretty obvious you are missing something. These physicals range from lung capacity to hearing and everything in between. This could also fall under the whole injury to self clause, and possibly get you into trouble. There is a good chance it will effect your strength and body weight unless you take drastic measures. Most who do this, end up wanting some sort of hormones or they feel terrible and they make it easier to stay in shape.