One student grading other students' assignments in the same course? In the US, can a student who is already enrolled in a course grade homework assignments of all other students in the same course (but not actually accessing and changing academic records)? Is it legal and compatible with academic integrity?

Two of several issues that I'm concerned about are:
1. He has not actually done his own homework (because homework submissions are not recorded).
2. By comparing my paper with other students I wasn't able to observer a consistency in grading. Actually initially I found who has graded our homeworks based on a pattern of inconsistency in grading and also inappropriate comments on my paper.

However the professor rejects my concerns by stating that he has overseen and reviewed everything himself.

In this page from USC.edu it is stated that "Please note that it is not possible for you to be both a student and a TA within the same course. Federal law [FERPA] and University policy both specifically prohibit students enrolled in a class from being able to modify their own grades or to view or modify the grades of other students enrolled in that same class." However as pointed out by Bob Brown, Supreme Court allowed in-class peer-grading.
A student grading other students in the same course is unusual, but certainly not illegal.  As to whether it is inappropriate, I would consider two cases:


Sometimes professors ask all students to do part of the "teaching" responsibilities for a course, whether that be lecturing, grading, creating course notes, etc.  The theory of this is that it forces a deeper engagement with the material, and may help prepare further skills.  When grading or similar is done by a student or other students for a pedagogical reason like this, I see no problem, as long as the professor takes into account the potential for quality variation.
If an individual student is simultaneously a class member and a TA/grader, that is much more unusual, and generally a bad idea.  In this case, the pedagogical value of having all students engaged with the process is not there to balance the expected decrease in grading accuracy and quality.  There may be certain unusual circumstances where it is appropriate, and a professor can, in fact, organize things to compensate for the issues that you raise, but in general I would be highly dubious about this practice.