Ukrainian has just one past tense, to which English tense does it correspond?
There is no straightforward correspondence, the system is a bit different. It depends on context how you translate a thought.
I think this is one of things that you just have to figure out. And you will eventually, if you keep trying. Just don't get too frustrated.
Isn't this the imperfective past tense? If so, why is "what were you doing yesterday?" not accepted?
It is now accepted as an alternative. Although, Ukrainian imperfective does not always correspond to the English continuous.