"You borrow the table" should also be accepted.
Since there is no context, both answers ("a" or "the") should be accepted. Definitely.
Agreed. Still marked incorrect 12/23/17
Still not accepted April 13th, 2018.
Duolingo's blunder over "a" and "the" without context continues 6/2/2018.
Can 너 be actually combined with the polite informal ~요?
No, I don't believe so. This is just used because they haven't been using 반말 in this lesson yet.