You can't change the resolution but you might be able to emulate a lower resolution in some way, eg drawing rects or small sprites to give the illusion of bigger pixels (I don't know anything about the Atari you mention I'm afraid).
The palette is easier - just use the colours you want and don't use the others :D
You could use this tool to set the desired colours and maybe set the ones you're not going to use to black or some other colour:
https://aaronsnoswell.github.io/blog/tic-80-color-palette-tool