I would like to know why my Games are divided into several groups, and what I can do to ungroup them? I have only about 6 games I play, yet when I select Games from the Launcher I get 4 categories. I don't have that problem with any other desktop I've yet tried.

I believe those sub-categories are specified in each game's .desktop file (there's a Categories entry which tells the DE where to put them; other DEs probably ignore the more specific categories).

You can always set up your own menu structure by right-clicking on the menu and selecting Edit Applications and then rearranging the structure however you desire.