I have done all the setup for Freichat, but I have no idea on how to place Freichat on my pages. I would think I would have to set it's "Position" but I don't know which one to use.

You can use any position which is visible on your current template .

I find that certain positions for different modules cause problems. Also, I'd like the chat to float, like Facebook. I'm using the default Joomla template, protostar

It does float like facebook by default .