Could It be that our school is haunted..?

ghosts o.O

Mischief Managed! =P

On a serious note lol. Hey! Well that does sound like a mysterious chain of events. It could possibly be that some otherworldy presence was there from the way that you describe it. Or quite possibly, with the same chance or a tad bit less, there was someone else there or who was simply messing with you guys or had nefarious intentions. Since you say that you saw the faucet turn on by itself. It depends which type of faucet it is. If it is one of those where you have to turn, then you have a problem. While on the other hand, if you have one that automatically comes on then someone alive could have done it; however, since you say that just a faucet came on, I presume that only one out of the many came on so that means there could possibly be something there. However, you need to clairfy still how many faucets there were. If there was one and it turned on out of the many, maybe it was a malfunction. Although, since the lights came out afterwards, that can be seen more than one way also. Maybe the lights were coming to make sure so no burglars come in like they do at most schools such as elementary ones; or it was malfunction; or it could have possibly been as you speculated, a ghost.
Also, the person entering the cafeteria. It could have possibly been a random person checking in on the place, someone up to no good, or somebody who was dearly departed from this realm. However, you can't say based on there being a shadow. From what I know about ghosts, I have never heard of a ghost being able to cast a shadow. Therefore, based on that part of the story it may not be a ghost.
So my final judgement is that the mysterious being needs to be clarified a bit more. Did you see its shadow or did you see it in another way? Also, the faucet questions needs to be answered. Therecould quite possibly be something there, but a few more facts are needed.