Is the ILS CAT III the most technologically sophisticated navigation / landing system available for helping commercial pilots land a commercial passenger aircraft in severe and extremely low visibility weather conditions. Does the airport require special compatible equipment for this system to work properly?
Yes ILS equipment for CATIII is the most sophisticated across ILS systems. As people mentioned in comments there are another types of landing systems, which could be more complex. No it is not auto landing system.
It self CATIII is a category of a landing conditions.
Also take a look here What is different between a Cat IIIA, Cat IIIB, and Cat IIIC ILS approach?
ILS Category 3C is true 'autoland' with no limitation regarding Decision Height for landing or Runway Visual Range. It's not especially complex (the equipment is not technically challenging)but has specific requirements regarding the equipment fitment for Cat 3C.
MWLS/MLS (microwave landing system) was researched which had some advantages including lifting the need to approach in a straight line. Although truly more complex than ILS, ther advantages it offered were not considered sufficiently worthwhile to proceed. https://en.wikipedia.org/wiki/Microwave_landing_system
Today, the most complex 'landing system' is probably those based on GPS(GNSS). Several (smaller) countries have announced their intention to replace ILS provision with precision GPS or LPV approaches. This requires greater accuracy than unaugmented GPS can provide and this is achieved using Differential GPS and Wide Area Augmentation System. https://en.wikipedia.org/wiki/Differential_GPS https://en.wikipedia.org/wiki/Wide_Area_Augmentation_System
The result is the LPV approach. https://en.wikipedia.org/wiki/Localizer_performance_with_vertical_guidance
This is currently the most complex 'autoland' from a technical standpoint but still has DH/DA and RVR limitations, thus making it less 'complete' than ILS Cat 3C. It does not meet the ICAO Annex 10 precision approach standard.
Also see RNP, RNAV, LNAV, VNAV, PA, NPA, APV