Will you be eating? Це правильно?
Both options are correct.
'Will you eat?' is grammatiacally correct, but it sounds a bit unnatural in English. I would usually say "Are you going to eat?"
I can hear "Will you eat already" said a bit rudely or emphatically by a parent to a child.
I agree that 'Will you be eating?' is a better translation into English. It is a phrase you would hear in a restaurant or cafe or bar.