Your bike is not designed to pedal fast backwards. There is no guide to guide the chain on the cog and the tensioner on the derailleur will not work correctly in reverse. Don't pedal the thing backwards fast. Don't worry about what it does in reverse, only forward. There is no indication that anything is wrong with the chain except you are pedaling it backwards too fast.

It does sound like the bearings are too tight. Is it stiff in both directions?