Well then. I'll try to explain in detail.
When I try to make changes, my Mac asks for an administrator authentication wit a username and my password. At school it works just fine, but when I'm connected to any other network it reacts as if my password or username is wrong. Therefore, I can't change anything in my system preferences, my application folder or install anything when I'm not on my school network.
So, logging in: No problem.
Logging in as an administrator: Only at school.
I have a suspicion it's a keychain thing, but I'm new to Macs so I really have no idea.