Can a gold crown be adjusted once it has been cemented in place? Can it be polished if it gets scratched?

I recently had a rct and had a gold crown set on that tooth. It feels like it may be too high (even after 3 adjustments prior to cement). Can a gold crown be trimmed, so to speak, while on the tooth? Also, some cement was left on the crown, between my teeth. When I got home, I picked it out with floss. In doing so, a bit a cement visibly scratched the surface of my gold crown. Can this scratch be polished out? I appreciate any insight that one can offer. Thank you for your time