How can I attach a safety gate at the bottom of the stairs?
Could you attach a board to the wall, that spans the distance between the stud, and your ideal hinge location for the baby gate?   For an example of what I'm talking about-- as well as plans for a cool parallelogram baby gate-- see the following:  http://woodgears.ca/home/baby_gate.html  (Note I am not talking about the gate at the top of the stairs, that you see at the top of the linked page, but rather the gate at the bottom of the stairs.)