The car is the Behra Porsche. It is Ms. De Filippis, but she didn't qualify for Monaco in 1959, so the picture was obviously taken during practise. As this was it's debut event, I suspect that the aluminium bodywork was just freshly completed and not yet painted, explaining the the rather odd appearance - those are grinding/sanding marks from the fabrication, not dents.
(though according to some sources, it could be mr. Behra himself?)