Is it correct that I say to my teacher "would you please start the class 30 minute late?" if I want to ask him to change the time of class from 16:00 to 16:30. and what do native people say?
I would say "Could you start the class at 16:30 instead of 16:00?" The class is on time if it starts at the agreed upon time, so it's not "late" if you both agree to start at 16:30. "later than usual" also applies if 16:00 is the usual time. If the class could be scheduled to start at many different times, then there is no "usual" time, so "later than usual" would be confusing.
I would say "Could you please start the class 30 minutes later than usual?" or "Would you mind starting the class 30 minutes later than usual?"
I must say that it's an odd request to make of a teacher, and it might tend to get the response "No - why don't you just make sure you turn up on time?"