GM - Game Master: Runs a role play's setting, plot, and NPC's. May or may not have a GMPC.
DM - Dungeon Master: Same as Game Master, but technically a term used specifically for Dungeons & Dragons.
Low-Advanced: RP's in casual or advanced that have lower requirements than those of advanced. In every way identical to high casual, except used to make some people's egos feel a little better.
High-Casual: RP's in casual that mimic advanced standards without adhering to them totally and utterly. Technically an irrelevant carry-over from older times, but it comforts some people nonetheless to use it.

Posting speed is determined by each RP, though in general, free tends to be very fast with several posts per day, casual is multiple posts a week, and advanced averages out at around 1-4 posting rounds per 1-2 weeks.

Posting Round: Each time a GM posts, they typically advance the setting and plot, and react to what players have done. Thus, a new round begins every time a GM posts.
Posting Order: Usually done as common courtesy, each person posts once per Posting Round, in order to avoid a flood of posts. This usually only happens in casual and advanced, though, not in free.

A suggestion for Bunnita: Try playing as a player in a couple RP's first in your desired section, get a feel for how everything works on the site, and then make your own RP.