First question is more of legal stuff. My final is to create a fake webpage hosted by my University. Would it be okay if I use sublime text for this? I noticed there is a buy button, so I want to make sure that I am not skimming the developers for their software.
You aren’t having any monetary gain from using Sublime unlicensed. This is after all a project for a course. Not an internship or job. That is normal for a college student. Keep using it if you really like Sublime Text. After getting your first job, do consider buying a license in case you still find yourself using Sublime Text often.
Just for me you can learn everything at home.