Why can't it be "You're renting that?"
Yeah, or "You rent it?"
What's with "did you rent this"?
Can this mean both "renting from" and "renting to"?
Some people use it in both ways colloquially, but it is incorrect and could get you looks from pedantic people :) in fact, it's:
Both of the sentences for teaching "שוכר" in this section are "I am renting this" and "Are you renting that?". DuoLingo, surely you know it's easier to teach verbs when concrete nouns are involved!