Would braces scrape off the sides the crowns?

No, but. Difficult to bond braces to porcelain or metal. Sometimes it helps to make minute scratches in surface of crown to facilitate bonding. Crown surfaces can be repolished after braces are removed. You may be candidate for clear aligner therapy, but braces do a better job. In an ideal world, braces should be done before crowns. Talk to an Orthodontic Sprcialist.
No problem. First see an orthodontist for complementary evaluation. No matter what age you are, how complicated is your situation. They complete at least two extra years of schooling to practice their skills. You can get a traditional braces or invisalain and your crowns will be intact. There is no interference between crowns and braces. Congratulation on your new smile.