A TRACON Controller reported an aircraft failed to intercept the localizer and flew below the Minimum Vectoring Altitude.

Narrative

Aircraft X was vectored to intercept the ILS XXR at ZZZ via ZZZZZ and instead turned towards ZZZZZ1 which is the FAF for the ILSXXR making it an illegal intercept. I cancelled the approach clearance and vectored to intercept the Localizer as the pilot did not show the capability of intercepting via a waypoint. Rather than intercept the localizer they turned at least a mile off course. I queried the pilot and he insisted that they intercepted the localizer. I cancelled their approach clearance again as I thought it was unsafe for them; their patient; and the city of ZZZ if I did not as I was afraid they would crash into the city. I tried to get the Front Line Manager (FLMs) attention but they were busy at the Operations Manager in Charge (OMICs) desk. I had to issue a low altitude alert as the pilot was still descending and revector them around again. There was other traffic I had to engage with and was shortly relieved when the plane finally made it on the third attempt. I am hoping nothing happened with the patient or organ that was being transported because of the delays. Not sure of the currency requirements for Company X pilots but to not be able to do things I would expect a professional pilot to do is troublesome.