1. He was born in 63 BC.

2. He was born in the 63 BC.
(Which one is grammatical?)

3. He had lived by 63 BC.
4. He has gone to Brazil in 2000 AD.
5. He died in the 21st century.
(Are they all grammatical?)

1 is correct; 2 is not.

3 and 4 are not right.
He lived in 63 B.C.
He went to Brazil in 2000. (A.D. is not used here.)

5 is correct.