The only way to make a user an affiliate right now is to head to the Users page to select the checkbox for "Affiliate". That's a good idea, though, and definitely something we can consider for the future. You can go here to submit your feedback directly to our product team: https://portal.prodpad.com/18563
For changing the word, if it's on your external site pages rather than your admin dashboard there should be a way to do this using Themes. Happy to write up some instructions if you can send over a screenshot showing where you mean?
I don't see where to do this, can you help me find the affiliate check box?
Here's what the affiliate checkbox should look like:
To get there, from Support Your Students > Users find the user you want to make an affiliate and select the Edit option (to the right of the screen).
I hope that helps!