Would пора року not also be "time of year" or would that translate differently?
Not sure if I'm correct, but the gender form of this question depends on the gender of the person speaking the sentence?
No, it doesn't.
The gender of «моя» is choosen according to the gender of «пора» 'season'. Since «пора» is feminine, the adjective-like pronoun «моя» and the adjective «улюблена» are feminine too.
Дякую! Вас також! :)