What I would suggest if your friend is buying on your behalf is to cancel the subscription as soon as it's paid for (you'll still be able to use it for the year!). Then also delete the card from your billing pages (email me if you have trouble with this).
Regarding licensing, send me an email if you have any specific queries but licensing is changing for Construct 3 slightly in that any registered business (sole trader, LLC etc etc) must buy a business license and is not permitted to buy Personal. Again, email is best to answer specific queries.
Thank you. I think I'll do it the way you suggested. Regarding the invoice, I'll just buy it for myself then for educational purposes so there will be no registered business involved.
I'll have an other question that just popped into my mind: Can I use my license on multiple computers at the same time? For ex. I have a completed project opened on my notebook for helpful glances, while I'm teaching students using the notebook the school provides?