If I uninstall Final Cut Pro X, will I lose my events and projects?

The Events and Projects are completely separate from the app so they will be completely safe if you uninstall it.

The easiest way to uninstall completely is to use this excellent free app

http://www.digitalrebellion.com/fcsremover/

You should also be using the latest version . . . FCP X 10.0.9

You have to update the software. That version will not work with 10.9.

Does this still apply? My FCPX won't open. It keeps getting stuck at "restoring window layout." I have tried to delete the "layouts" folder and that didn't help. I read uninstalling and reinstalling could solve the problem. But I don't want to lose my work.

Yes, it still applies. What version are you using?

Russ

edit: fix two typos

Your media, Libraries, Events and Projects etc. are all kept separate from FCP X so trashing FCP X will have no effect on them.