Student or Learner
I wonder if there is any difference between "1" and "2"
1. Do you know he is a singer?
2. Did you know he is a singer?
Both sentences are grammatically correct though it is much better to say in the second sentence: Did you know he was a singer?
Anyways, the sentences that we have right now are:
Do you know he is a singer?
Did you know he is a singer?
The frist one:
The person who is asking you this question wants to know now whether you really know or not that someone is a singer.
The second one:
The asker wants to know if you knew in the past that so and so is a singer.
To explain this latter point let us have the following example as a context:
A: I met Mr. X two years ago.
B: Really! Did you know then that he is a singer?
A: No. I have just been told that.
Hope it is clear.