Is there a way to make FB completely private from all, just so I can play the games that require Facebook?
Yes there is. Go into settings and make all post visible to you only. I do it on all my pictures. If I choose to share anything I click on the post on the upper right corner "share with friends". Yes it can be done
yeah ... set your security to "friends only", then don't add any friends.
Some one is embarrassed to play Facebook games :)