1. I think it could work in 1 of 2 ways:
a. Stat orientated
The lowest amount of turns in a victory, highest level, highest %killed in a victory, etc. of all your games is recorded, and each one contributes to a total, which is then turned in to a rank. For example, for every %killed in your best victory, you gain 5 points, for every level up your character went through in your best game, you gain 25 points, for every monster you killed in your best game, you gain a point.
In this case a low rank would be achieved with 100 points, whereas 2000 would be incredible.
b. Goal orientated
In this one, you gain points by achieving certain goals, like beating the game on difficulty 4, or defeating 300 enemies in a single game, or visiting all secret levels in the game, or by beating JC (whether you survive or not), etc.
2. It really depends on whether you want long time players rewarded, or skillful players rewarded.
Long time players are rewarded:
Enemies killed
Cybies killed
Melee kills
Stairs gone down
Skillful players are rewarded:
Highest level on each diff
Points gained in a single game
Highest %killed in a victory
YAAM victories
I suggest using both, having a rank like this:
Sergeant (skill rank) Thomas, a very experienced soldier (long time rank), defeated the Cyberdemon on level 20 on Phobos's base. (I'm allowed to dream aren't I?)
3. Simply for fame, in my opinion. Maybe an unlockable or two, but I would rather say General Thomas killed the cybie, rather than Marine Thomas, and would work for a better rank simply for that.
4. Yes, but not one that you need to add with top priority. Put it in when you get the time.