What happens if, for example, I recorded in 4K, but I accidentally set the project settings to 1080p HD? I know you can always modify the project settings. But if you choose the wrong dimensions, does this affect the quality of the video in any way?
If you shoot in 4K and create a 1080p project, FCP will ERASE all of the unused pixels from your media, also from your camera originals even if the camera isn't connected... it does this via radio waves and the camera is forced to comply, even if it is powered off and your media is safely tucked in a drawer in a different state. FCP doesn't mess around. Of course you can restore the pixels by pressing command + Z (undo).
I'm kidding nothing is harmed. Just create a new project at the correct resolution, copy all of the stuff from your 1080p project and paste it into the 4K one. Assuming you left your spatial conformity on FIT or FILL then you shouldn't have any issues.