You should also check that both brake arms are freely pivoting.
Your brakes do have a form of quick release, you can unhook the noodle. Do this and see if both arms are free to move (they have a return spring).
Once you have established the arms are moving freely, hook the noodle back up and then you can adjust the centering using the screws near the pivots.
How far the pads retract from the rims is a function of cable tension, so if you let off some tension to back the pads away from the rims, you will have more lever travel before the pads engage, but this is not a bad thing as you can exert more force with your fingers as your hands becomes more clenched, just make sure the levers will not bottom out on the grips before the brakes are fully applied.
While your working at this, a good inspection of the condition of the cables and housing is in order, especially on an ex-rental that may have not had the greatest of servicing in its former life.