You can use the crop tool to get rid of the appearance of the stuff as I understand the issue. However, you then either have to use redaction or just print to a new PDF to remove the cropped material from the PDF. Used to be that the Reduce File Size would remove cropping, but I think that only lasted 1 version with the cropping feature.
Depending on the scans, you might find you can crop all even and all odd pages separately to meet the needs in a more automated way. I would still scan through the document to be sure you did not cut something off.
In terms of your use for scanning, it varies a bit. In many cases, it is considered acceptable for personal use. Limited copying is even found acceptable for classroom use. Full books (or substantial parts) for classroom use usually require the approval of the publisher. This is not a legal opinion, but what I remember our library indicating. You school librarian may be in a good position to give you school policy on such scanning based on the school position. I would be looking into our school policy if I wanted to scan a substantial portion of a text -- I know they do have a policy.