If you are leading a game, is it ethical to capture your opponent's pieces one by one or go straight for checkmate?
There is no rule or law that says that you have to try and checkmate in as few moves as possible and so there is no ethical requirement either.
In fact, if there are just a few pieces left on the board and you are very short of time it makes a lot of sense to take all the opponent's pieces as quickly as possible and only then worry about how you are going to checkmate.
Otherwise if you run out of time while your opponent still has some material left then you are going to lose on time. If your flag falls after you have taken all their pieces then you still get a draw.
The USCF Code of Ethics states that the following is unethical:
Deliberately failing to play at one's best in a game, in any manner inconsistent with the principles of good sportsmanship, honesty, or fair play.
I would take this to mean that if you have a mate in 1 and you see it but purposely don't play it, you're being unethical. However, I would not take this to mean that you cannot take your opponent's pieces if this is a legitimate attempt to win (or prevent losing on time.)
If a football game was lopsided at halftime, wouldn't it be ethical to call the game?
Since chess has a resigning option, I don't consider any move as unethical. I consider an opponent who doesn't resign in a hopeless position as someone who deserves to be tortured, and it allows me to practice technique. So promote to all knights and practice the unusual mate.
It depends on level of play and seriousness. If this game is a tournament game but lower rated, I would be happy if my opponent was playing around. This would allow more stalemating chances.
If I seriously didn't want to endure it, I could always resign. If this was a grandmaster game or just a high rated game that was taken seriously, it may be seen as disrespectful and unsportsmanlike to do so.
Just like how there are no real rules against offering a draw, it could be seen as rude to offer a draw when you're clearly losing.
Of course if you're playing a casual game, you can do whatever you want. When I play with my friends I would often give up all my pieces and underpromote some pawns to do fun checkmates like 3 knights and whatnot.
Why would you choose to not choose to checkmate right away? You are wasting both your time and your opponent's time by not doing so. Tournaments take place in short periods of time, so using that time to keep up your ability to play is important. Unless there is a time constraint, and you are trying to ensure that you will not lose by running out of time, you should checkmate in as few moves as possible.
It doesn't hurt to ask your opponent if they'd like to resign or keep playing. I beat a number of better players when they got well ahead and made mistakes, and I lost many games the same way.
Also, weak players don't get to really study desperate endgames if they're always resigning. One of my chess partners used to consistently draw me into a stalemate when I was well ahead, instead of resigning. If he'd just resigned, or if I'd just wiped him out, I would have never grokked that option.