You'll always have a corner case or another. I wouldn't care about personal usage users.
Case 2 clearly falls into the free usage policy, but in case 1 if the school is requiring students to install this software in their school-provided hardware as a way of sidestepping licensing fees I think they are stretching it a bit.
I agree with the first, but the second doesn't qualify. If the person using the software (a friend) owns the computer where the software is installed (my friend's computer) he qualifies for the free license. I don't think it matters who actually did the installation.
1. Does that mean a student would have to pay to install it on their school computer? Or maybe a school provided laptop?
2. What about personal installs for other people? Not as a business or service, but merely on a friend or relative's computer?
Because in theory, both of those would come under 'someone else owning the machine', but they'd also be seen as personal usage by any rational person.