2. Okay, I got it now. - This is correct. It's a shortened informal/colloquial form of "I've got it now." So even though it may appear that it is the past, it actually isn't. By saying "I got it now.", the speaker is really saying "I've got it now."
3. Okay, I understand this now. - This is correct.
4. Okay, I understood this now. - This is not correct. I would say that, in English, when we come to an understanding of something, it would be considered a state of mind. Therefore, the simple present is used to say that we now understand something. It could be viewed as a general truth or fact. "I understand now."
I know it could seem strange to understand something as a result of an explanation that someone gave - in the past, and then use the simple present to express that. However, that's how it works in English.
Now, it would be possible to say, "I understood." in another sentence or context.
I understood what you meant after you explained it to me. - completed the action of obtaining understanding - simple past
We can contrast that sentence with this:
Thanks for explaining that to me. I understand now. - now maintains an understanding of something for all time - simple present