Hi szhorvat I’ve answered the questions I can from your list hope you find it helpful 
Have a look at changing the colour of Instructor usernames or adding a tile etc. you can find a guide on how to do this here.
Can’t you just create a category for each semester or something then create groups which can only create/reply/see that specific category?
In the /admin/users/list/active there is an ‘Export button’
There is the full name required site setting
I’m quoting this from the Discourse.org website
If you are legally recognized as an educational institution we offer an 85% discount. If you are legally recognized as a non-profit organization that is exempt from federal taxes, we offer a 50% discount. These discounts apply only to our basic, standard, and business plans, cannot be combined with other discounts, and must be paid through a debit/credit card monthly or annually. Please contact us after starting your trial and we’ll add the discount to your account.