Each of the 3 departments has several users.

1. Some users are more than one department. Can users have multiple roles?

2. If I assign page permissions will sub-pages inherit permissions?

3. If the football department creates new pages, will their newly created page take on permissions of their other pages, or do I need to set permissions for every page that anyone creates?

Thanks for your time, Syam!

Here are the answers to your questions.

1. Yes. https://wpfront.com/user-role-editor-pro/assign-migrate-users/
2. No, those needs to be set separately.
3. There is no inheritance. You will have to set them manually. You can use Bulk Edit to set them together.

Thanks

Syam