"Will you hire her?"
Translation:Werden Sie sie einstellen?
jemanden einstellen is to hire an employee. It's not used for cars or objects.
vermieten is to hire out (i.e. to lend something in exchange for money).
heuern is not a common verb; I'm not sure when I would use it. anheuern might be used for employing a sailor, but it sounds a bit odd outside of a nautical context.