No, its right where it should be.
Congrats on figuring out the password
To answer your questions in order:
Yes, the activity will be logged. The question is whether you have a through admin that checks all the logs, and who was on when. Yes, you can be punished for this in most schools, in some places it can even be escalated to a federal crime if they have reason to believe that you were interfering with things such as grades. People that are as worried as you about getting in trouble probably shouldnt be doing such things, so I would suggest that if you want to go the safe route simply never log into that account again. Ever. If you do so at home, they can trace the IP address and the police might get involved.
Keep in mind that I tend to go with worse case scenarios, but it is possible. Also, dont brag to anyone about anything you have ever done (except in xatrix of course) in your schools system, it will come back to bite you in the ass.
Abandon all hope, ye who enter here. -Socrates
The only thing I'm worried about is that: if I go on either of these accounts on the network can it be logged/traced e.t.c and can I be punished for it. I am hoping to do very well in exams e.t.c and don't want to be kicked out of school. The other thing is, there are quite a few cameras around the school so I will have to be careful, thanks