is it safe to drill into this wall?
If we get to guess, I'd say the wire is somewhere in the first stud bay on the right-hand wall (as you're going down the stairs). A stud scanner with a 'deep scan' mode might give you a sense of where it is. (And it might not extend above the conduit height.) Look outside to make sure there's no coach light on the exterior wall above the door.

As for studs, you'll certainly find some in the corner. 16" is a good guess only when you've found others in an set. Outlets and switches almost always have a stud on one side, so that might help with the measuring. 

I doubt you'd crowd the stairwell with a low platform, but be aware that residential code in the US usually requires at least 6'-8" headroom from the nose of a tread to the bottom of a platform.