Undergrad students grading other undergrads: ethical, professional, or even legal?
It's a fairly common practice at some universities for older undergraduate TAs to grade younger undergraduates' work. My undergrad institution relied heavily on this - it's perfectly legal and ethical SO LONG AS you, the TA, do not discuss one student's grades/work with another student. More generally, a TA in the United States is bound by FERPA as to what is legal or not.

If you're concerned about not knowing what to mark as wrong, consider asking the professor you are grading for for an answer key or an example solution set. They may be unwilling to give this to you outright, but hopefully they will at least walk through an example with you and point out what they're looking for in a fully correct answer.