Can i put my high Sierra backup on my Catalina Mac book air

Sure, that's what Migration Assistant / Setup Assistant are designed to do. Read Set up your new Mac - Apple Support.

If you already set up your new Mac and are using it, then use Migration Assistant: How to move your content to a new Mac - Apple Support.

If you want to restore just your Photos Library and Music Library, restore those individual items from Time Machine: Use Time Machine to restore deleted files or older files - Apple Support.

No, not unless your MacBook Air was produced before Sierra was superseded by High Sierra.

You can migrate content from a HS backup when you initially set up a new MacBook Air, or with Migration Assistant subsequent to setting it up.