1. He is A teacher and A dancer.
2. He is A teacher and dancer.

Are they correct?

Thanks in advance!

Question

1. He is A teacher and A dancer.
2. He is A teacher and dancer.

Are they correct?

Thanks in advance!

Answer

2

To avoid the cofusion just memorize the following example:
The bank was robbed by a teacher and dancer <= one robber.
The bank was robbed by a teacher and a dancer

Answer

1 is more common. 
2 is less common but understood by everyone. I do not think it is ambiguous.
You may be aware of the "distribution law of multiplication" from 5th grade: 
      n(a + b) = na + nb.   Example: 5(2 + 3) = 5(2) + 5(3) = 25
The 5 is distributed over the terms.
Like your A is distributed over the nouns.
Same same: He is a great teacher and dancer. Means he is great at both.
This can be emphasized with "both", therefore:
3: He is both A teacher and dancer.

Answer

The first 1 is correct. If you say either, no one will correct you, and I imagine that plenty of native speakers will say the second one not knowing they aren't saying it right.