These are all correct. They make sense. I would say "I'm not getting it." Or "I don't get it." or "this is not making sense to me." I had a university professor who would often ask "get the idea?" So you could say "I don't get the idea" or "I'm having trouble grasping this concept/idea." If you want them to explain differently you may ask "Could you please, explain this another way?" or "Is there another way of looking at this?" You could also ask "Could you please repeat that, I had trouble getting it the first time?"

"I'm sorry, I don't understand."

The best phrase to use would be, "I'm sorry, but I didn't understand." Then ask her/him to explain it again. This is your teacher, remember. Using colloquial speech may be a little too blunt, or even rude.

The better way to ask is, " I am sorry, I cannot understand what you say, can you please explain in detail?"