Is it correct to say "know your place" to someone that is being rude to an elder person or someone important? And are there other phrases that can be used?
I'd probably say, "[Please] show [some] respect." To me, "Know your place" is somewhat old-fashioned and has connotations of a master – servant relationship or of a class-bound society.
Sometimes a humorous rebuke (such as "I wish I were your age and knew everything") is more effective than a solemn one, but it depends on the person and the occasion.
You can always use, with any person who is being rude to just about anyone;
"You can catch more flies with honey than with vinegar".
He/She might even learn something from it :) .
But its not specifically to what you asked for.