1. He is a good actor as much as he is a good singer. (Is this sentence correct?)
No, that sentence is not correct. Here is how it should be revised:
(1a) He is as good an actor as he is a singer.
2. He is as much good in acting as he is in singing. (Is this sentence correct as well, though It may differ from the first one in meaning?)
No, that sentence is also incorrect. You need to delete "much":
(2a) He is as good in acting as he is in singing.
3. He is as good in acting as he is in singing (Actually I cannot decide whether 2 is correct or 3 is).
Yes, that sentence is correct. It matches my revision of (2) above.
3. As he is a good actor, so he is a good singer. (Is this correct and similar to the any sentence from 1,2 and 3?)
Yes, it's OK. My preference would be to begin with "Just as," though.