Can I delete my Apple ID and make a new one?

Answer 1

Yes you can.

First you must go through all of these steps:

1. Remove devices associated with your Apple ID
2. Disable Find My iPhone, iPad, Mac
3. Sign out of ALL THE THINGS!
4. Delete your account using Apple's data and privacy portal

You will have to sign into your Apple ID account (https://appleid.apple.com/#!&page=signin) to do this.