How many points down should you resign?

White can mate black in three moves if white is to move in the position above. 

Indeed. For experienced players, to be down a piece with a rook on each side is sometimes reasonable to play on. A rook vs five pawns maybe not soo much. To be down a pawn with rooks on is drawish, whereas being a bishop up but a pawn down is doable. Point is (heh) in a practical game, confidence in yourself is crucial. After all, it's only a game. I pretty much know when the curtains are coming to a close. But only you know when you are at your limit. Better to resign when you feel "it's time" and move on, rather than play on with a gloomy outlook.

"How would you know the engine's evaluation without using it to help you make the decision to resign?"

This question really does answer itself. Many players use computers post-game for analysis. I'm one of them, and I assume SmyslovFan is too. You'd assume that someone who cheats by using a computer during a game would not comment about computers in the threads. Also, I wouldn't expect him to find himself worse off in position than the material suggests, quite the opposite in fact. People who use computers will make positional moves that make no sense to a similar rated player, such as deep positional sacrifices.

Why do we have time controls at all? The reason is to stop unsporting people from playing too slowly. If everyone recognised that you have a moral obligation to play within a certain time there would be no need for time controls. Therefore the fact that some people use time controls to try and leverage a win is an example of unsporting behaviour imho.

Oh come on, a game between grandmasters can be won on time by someone in a clearly losing position. Mikhail Tal would often make suboptimal moves when his opponent was in time trouble just because such a move would require more calculation.

If you don't want time to be a factor in the result, play correspondence (daily) chess and take all the time you need.

I always, always resign when my position ends up bad, or I've made a blunder that loses me a piece. There is not point in dragging on a lost position, expecting the opponent to make a mistake so I can catch up. It's not very polite.

don't resign, just attack wildly at your opponent so that one of you gets mated