A:
Oh welcome to why Microsoft stock is so expensive... I like most of the Microsoft products but hate how they stick the consumer with any cost possible. Yes, unfortunately, you will have to purchase a separate operating system for each computer; or you can purchase an operating system card that allows for multiple computers (cost is obviously more), last I checked it allowed the consumer to upgrade up to 5 separate computers.
I recommend you have your mom try Windows 8 before purchasing it; I and everyone I work with find that 8 is an absolute pain. My mom hated it, and I had to pay $100 to remove 8 and put 7 on her laptop so that she would use it again.