Is it legal in the US for a student to download a copy of a textbook, to study?
In general, it is not considered fair use to download the entirety of a textbook, regardless of whether or not you're a student or enrolled in a class using the textbook. Fair use normally is considered to extend to making copies of small excerpts of larger works. For instance, you could copy a particularly relevant figure from a book, or a quote from a textbook or reader for use in a class discussion.