I can leave a mark, but I cannot cover up. People use me to Select importance.

I move from house to house, but I always stay outside. You can find me by the shore for my home is the tide.

I can cover kingdoms but not be touched or seen; Rulers judge me yet lovers endure me. What am I?

A mountain's peak, or leader's conference meeting. Where those can seek, an accomplishment, not fleeting.

Remove my first for paintings, music, cinema, and more Or drop my last for liberating personal transport Subtract my third for common pets that gorge on fancy feast But all as one, I'm box and wheels once pulled along by beasts