Installing fresh Mac OS X - what about license?

The key to your stuff on your drive is your user ID (and if encrypted the written down key which you should have) and for iCloud your Apple ID.

The OS license is assumed as you are running it on an Apple computer. So don’t fret about it.

Hopefully you have been good backing up your stuff using TimeMachine if you have during the OS install it will ask you if you have data to migrate this is the point you need access to your backup and when asked to replace the current User account I would do so and make sure to fully install all the user data, that way you will be back to where you where.

But we do have a wrinkle here as the thumb drive is not the macOS you had installed I strongly recommend you have your friend create a new drive with Catalina. Access it from here How to download macOS and follow this guide to convert it Create a bootable installer for macOS