Facebook videos playing in low quality
I think this could be due to 2 reasons:


The videos you are playing are not available in a better quality. Or;
Facebook thinks that your connection is slower and hence reduces the playback quality. 


You can see that it is not the 2nd by manually choosing a playback quality:

When you play a video and tap on the player, a gear icon should appear. And here you'll get the quality options.
Consider changing it from Automatic to one of the available qualities and see if that improves the playback.