"I was not sleeping."
Translation:Я не спав.
Is this gender-specific? As a woman, would I say "Я не спалю?" (or something like that?)
A verb "to be" - "бути" isn't necessary in Ukrainian for past and present tense, only for future in some cases. To express right tense of the action you should know endings of the verbs. In this case being used past singular masculine ending - "в". For check if you put ending right, use following questions: (що робив) я спав - past tense, (що роблю) я сплю - present tense, (що зроблю) або (що буду робити) - буду спати або спатиму - future tense.
Hope it will help you, wish a good luck :)