Can a Professor move a class an hour earlier? My professor moved class from 1:30 to 12:30 and I missed class and a big research presentation i was supposed to give.  Is he allowed to move class like that?
It depends on your University's policies. At my University, professors are not allowed (see [1]:34-83). Your University might have some stipulations regarding this (e.g. was it done with due notice? what happens to students who were absent the day it was decided?). 

Your best choice would be to check the policies and see if you have the right to give your presentation during office hours or at another time.

References:
[1] http://senate.psu.edu/policies-and-rules-for-undergraduate-students/34-00-course-scheduling/#34-83