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  3. What Happened Here?

My opponent flagged, but it was still a draw even with material on board for me. Why?

My best guess is that it is impossible to mate with the king and knight vs the queen and king.

Pure chess rules. It is impossible to checkmate your opponent, even in his worstest play, in this case.

True, low on time + an annoying knight = draw.

If your opponent flags, you are only given a full point if you are still able to deliver checkmate in some possible future legal position.

Because there is no way to deliver checkmate with your knight against his king and queen (even if black's king is in the corner—try setting up checkmate with the given pieces on an analysis board if you're skeptical), you cannot be given a full point, even when your opponent flags.

Yes, as others already said, if your opponent flags, you only win if there is such material on the board (not only yours, also opponents, that can somehow legally deliver your opponent a checkmate. I will describe later what I mean, now let us get to your case. It is draw in the worst case. The closest you can get to win is this:
8/8/8/8/4N3/7K/8/q6k b KQkq -

Black is to move and plays Qg1??. Your best attempt would be Ng3+, forcing Qxg3 which leads to draw after Kxg3. Otherwise a pretty much lost position.

Now consider this position:
8/8/8/8/4N3/7K/8/r6k b KQkq -

Almost the same, just opponent has rook instead of queen. Should still be an easy game for black, but in this case, white can actually checkmate black with only a knight. Black now plays Rg1?? instead of Qg1 in previous case. This time, instead of Ng3+, we will play Nf2#.

This said, it's not only your pieces that determine whether you win or lose or draw when opponent flags out ;). Hope this was helpful.

You are only awarded the best result possible from the board position when your opponent runs out of time preventing the continuation of the game. In general, this is a loss for your opponent as you often have the ability to generate a checkmate on the board with the material left. However, in positions such as shown here, it is not possible to generate a checkmate with the material left and therefore the next best result for you, a draw, is awarded.

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