1. The girl is aged 13.

2. The girl is 13.
3. The girl is 13 years old.
4. The girl is at the age of 13.
5. the girl is at age 13.

(Are they all grammatical and the same? Is #1 correct?)

2 answers

#s 2 and 3 are fine. The rest are highly unusual and not used.
Maybe 2 or 3 but 4 is okay too