If it runs Lion it will run Mountain Lion. If you are using another persons copy of Logic Pro then that is illegal. We cannot advise you regarding that except to recommend you purchase your own copy or see if there is academic pricing available through your university.
Additional partitions will not "mess up your Mac." It will simply reduce the amount of space in the partition from which it is derived.
I didn't realise it was illegal, my mentor used to use my iMac for Logic all the time as his computer failed, I suggested that he could use my iMac until he raised enough money to buy a new computer. I would use it for my studies, and he would use it for recording his own music.
I only ask about the speed difference as the reviews on the Appstore keep claiming that there is an significant drop in performance from Lion.
Couldn't say about speed of Logic. I don't use it. Given that Mountain Lion is as fast or faster than Lion I can not comment of the so-called reviews.
Surely, you know that if do not pay for commercial software and use someone else's copy, that constitutes piracy. Much the same as my putting my name on a piece of your music.