@Adwaya Hi! I actually don’t know much about online orientation, however since I’m a peer leader at orientation, I’llask one of my supervisors and see what they say. Since this is a pretty specific question, I’ll inbox you the answer. 
The math placement test should be taken at least 3 days before your orientation program. Since you are taking an online orientation, you should probably just take it as soon as you are able to, that way it’ll be out of the way.
Registration for classes is actually an online process. Normally students register for classes during orientation, so I assume there’s a special time for people participating in online orientation to do that. I would contact the orientation office for more details.