Is it rude to resign, or should I play to checkmate?
It is definitely NOT rude to resign! If you are tired of playing and want to start a new game, you can definitely resign, that's what the button is there for!
You might also wonder, is it rude to keep playing in a lost position? This also is not rude, and some chess coaches even encourage their students to always play to checkmate, not only for the learning experience, but because beginners often blunder, and you never know when your opponent might mess up!
What IS rude, is stalling. This is when someone who is in a lost position delays the game as long as possible to make the other player wait! As long as you are not doing this, you can feel free to play on, or resign, whichever you decide!