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.

As to the question in the title it is certainly ethical, professional, and legal. More than that, in the US at least, it is extremely common (in my experience at both public and private universities). However, undergraduate TAs should be handled by faculty somewhat differently since the potential for conflicts of interest which arise from grading students in their peer group is higher.

Carnegie Mellon has some very nice resources available on their website for both undergraduate TAs here and for the faculty supervising them available here. One of the points in your question about which you seemed particularly concerned was grading other students' assignments. An interesting point from the document for faculty above is the following instruction for faculty:

Provide clear, explicit grading guidelines to undergraduates involved in grading and evaluation. Without clear guidance, undergraduate TAs tend to be tougher graders than faculty.

So, I would say if you are in doubt about how to grade a particular assignment, you should not hesitate to ask for more guidance from the faculty member you are grading for. You should also certainly speak to your faculty supervisor if any conflicts arise. Another quote from the above documents on this point:

We expect the undergraduate TA to be neutral in teaching or grading, but we must understand that this is a very difficult ideal for anyone to meet. Following are some tips for averting such challenges:

• You and the student should work together to identify potential conflicts of interest. Before the start of the semester, review the list of students with the undergraduate TA. Faculty cannot simply assume there will be no problems; likewise, undergraduate TAs may not be aware of these difficulties or their potential severity. The undergraduate TAs have interacted with the “potential conflict” students prior to the class, and may continue to do so for many semesters afterward. In our survey of undergraduates involved in teaching, a significant number of the students identified problems of this nature.

You might also find this article from earlier in the year in USA today interesting. It's just a quick overview of the social aspects of being an undergraduate TAing for undergraduates.

Undergrad students grading other undergrads

I've seen much more: undergrad students grading grad students, grad students grading postgrad students and research scholars! Before my opinion I'll state the basic concept:

Any of those who are qualified with the course subject are considered eligible to evaluate the answer scripts of the subject. This includes those who didn't complete the degree per se. Undergrad students who have completed the subject are said to have more up-to-date knowledge in the subject enough to grade other students of the same.

As a PhD research scholar myself, I felt the same. However, this even occurs in IITs (Indian Institute of Technology, the most prestigious institution in India). Hence this is something to accept with. I'll be happy enough of the grader who doesn't know the subject don't grade my course work irrespective of age or degree.