Also referred to as a gamemaster, the game manager (GM) acts as an organizer, arbitrator, and moderator for a simulation or role playing game. All simulations have at least one GM, but most have at least two. Having a second GM allows for the primary GM to take breaks when necessary or for a second opinion should one be needed.
Generally speaking, they run the simulation. Typically the simulation's commanding officer (if it has one) will be the lead GM, but this is not always true. Some of the duties that GMs carry out are listed below.
Depending on the simulation, different GMs may perform different tasks. Some simulations make no distinctions between tasks and who is allowed to do them while others are more strict in their distribution of power. For example, a simulation may have an assistant GM whose only duty is to maintain the appearance of the simulation website. That GM might be referred to as the webmaster or webmistress.
If you start your own simulation, yes. Otherwise, appointing GMs is up to the existing staff of any given simulation. It is best to never ask to be made a GM; many GMs find this to be brazen and suspicious. It doesn't matter if you're a GM on other simulations because every simulation is run slightly differently. A GM team must be certain that a new member works well with them and understands both the software used to run the simulation and the content of the simulation itself.
We're working on it. Azmaria has been working with Kuro-chan to develop a Game Manager Academy. In the meantime, both Bravo Fleet and Theta Fleet offer commanding officer academies, which may suit your needs. You may also inquire about such training with Obsidian Fleet and Pegasus Fleet.
You also need to know some basic, and preferably extended, plot development skills.