Is it possible to run the module on the left side of my site and also as a menu item on my site? In the module settings if I change the position from FAQ to left, then the module no longer appears when you click the FAQ link on my menu, and vice-versa. I want the module to run on the left of my site at all times AND also be linkable from the menu. Any suggestions?

Sure,

you just need to create a copy of the module, have one in position left and one in positon faq. Then you will have both. You can copy the module in the module manager.