Virtual Villagers allows you to have 5 games at a time using the Change Player function on the main menu. If you want to have more than that, you can accomplish that by moving the savegame files between different folders. If you do that, though, you have to be careful to keep track of which ones are which and avoid overwriting them, since the files will have the same set of names.

The mushrooms and Island Events are basically random, and are not player controllable. They also are independent of game speed or difficulty. The Island Events generally occur about once a day after the first few, but if you don't check on your games very often, they will happen much less frequently. I have games that have been running since July and I still get Island Events in those games.