Learn Polish: Kiedy będziesz mył podłogę? Zaraz ją umyję! - When will you be washing the floor? I will wash it right away!

This is the exact difference between imperfective and perfective verbs in the future tense! Myć is imperfective, focusing on the process. To make its future tense, you need a form of być (will be) plus the past tense form mył. Umyć is perfective, focusing on the finished result. Because perfective verbs already imply completion, their standard present tense conjugations automatically refer to the future. No być is needed!

Could the person answering have said Zaraz będę ją mył instead?

Grammatically, yes, but the meaning changes slightly. Zaraz będę ją mył (imperfective) means "I will be washing it right away" or "I will start washing it." By choosing the perfective umyję, the speaker is promising "I will get it washed and finished right away." It sounds much more reassuring that the chore will actually get done!

Why does the second sentence use the word ją?

Ją is the Accusative (direct object) form of ona (she/it). In Polish, podłoga (floor) is a feminine noun. So, instead of repeating the word for floor, the speaker uses ją to mean "it".

How can we tell the gender of the person being asked the question?