Tons of solitaire games the App Store. My current favorite is FreeCell by Branium. They also make the more traditional Klondike style Solitaire.
If you are talking about playing games in FaceBook itself, you can't do that in the app or in Safari (the browser). You 'might' be able to do it with the third party browser Puffin. I'm not sure. There is a free, trial, version you can check out to see if it works.
If it does work, don't expect it to work as well as using a desktop. The FaceBook apps/games are not designed to work with a touch screen device.
FaceBook has separated its main FaceBook app and FaceBook Messenger. For a while you could send and receive messages with either, but they have put and end to that. As a consequence they are on a major ad blitz about FaceBook Messenger, trying to get people to download and use the app.
Expect to see an ads for it anytime you access FaceBook on a mobile device. At least for a while.