I tried to get the answer from microsoft but could not find any. Is it illegal for me to give a copy of windows 7, that my mom legitimately bought for me from best buy, to my mother for her to install it on a computer that I assembled for her, and living under the same household? Also I do apologize If I am breaking this don't rule: "Ask for help pirating, cracking passwords, or bypassing copyright protection." I'm not asking how to bypass, just if it is not a good thing to do.
This is somewhat of a confusing area, so it's OK that you're coming to us with a question.
Technically speaking, if you build a brand new machine and you want to install Windows on it, you need to get a System Builder or retail copy of Windows 7 (system builder is cheaper).
It sounds like your mom bought you a copy of Windows 7 retail. If you have not installed that copy of Windows (i.e. installed and activated Windows with the accompanying product key) you may install the OS on any single machine you like. If you've already installed/activated Windows on a machine with the product key, then it is in fact against the terms of the license agreement to install it on another machine.