What will happen to anew user's account if he wishes to change his username after some months in the forum?

Done. Now only moderators, Donators, and VIP members can change their names automatically. Other members should contact me. I'll probably ignore your request if you have less than 50 posts (unless your posts are very good).

You can't. You can try PM an admin and they may do it, but they usually don't. You can just create another account  with that name if you feel like you need it.

Q: I want to change my forum username. What should I do?
A: You can either donate 50 BTC to become a VIP or PM theymos asking to change your username (although he rarely accepts such requests nowadays).

If the user has achieved a high rank in the forum, and choses to change his username, will the account be suspected of changing hand and be tagged for that?

Each user has a display name, which is the only name ordinary users see, and a username, which is what you use to log-in with. Almost always, they are the same.

If I change a name for reasons of appearance, then I only change the display name. The username remains reserved, the user can still login using the username, PMs can still be sent to that username, "search member" allows searching for the old username, etc.

If I change a name for reasons of privacy, then I change both the username and the display name. In this case, it is possibly hazardous to reserve the old username, since it allows someone to test for the existence of that username, possibly defeating the privacy benefit. If you're worried about being impersonated, then simply don't seek to have your username changed.