Your device may not have the capacity to play them. You also could need to update the device. Check in settings and check your facebook app to see if it needs updating as well.
Additionally, if you have other things open on the phone at the same time, even if they aren't active, they will use up your resources, making games not work well.
And lastly, your data plan with your carrier/service provider comes into play here as well. Unless you have data turned off and are accessing stuff via WiFi, the data connection could easily be your problem. Most accounts have limited data. The few that don't turn it off when you hit a certain usage, or don't charge you extra for going past the cap, will usually slow down the data speed drastically...