Cat I, II and III are largely aircraft operatioanal matters and determined principally by the decision height associated with the approach. The way the aircraft is to be operated, that is to say what equipment must be used and how much of the approach and landing must be conducted using 'automatics' is usually determmined by the aircraft operator (typically following the equipment manufacturers' recommended procedures and international standards) and approved by the operator's national authorities.
The ground equipment will be defined/authorised to provide a service that supports Cat I, II or III. The differences between Cat II and II requirements are small but both require more standby and back-up facilities. The surrounding terrain is also a factor as it can cause the signal to be disturbed. The equipment will not be authorised unless the transmitted signal meets particular specifications. The runway and approach lighting will also have to meet certain minimum specifications to support the various categories of appraoch. There is sometimes a trade-off between sub-standard lighting facilities and decision height which means that, say, whilst a Cat III approach might otherwise be possible an increased decision height means that only Cat II approaches are approved.
The dimensions of critical and sensitive areas are determined by the antenna array and the way that it radiates. Whilst there used to be 'standard' sizes, modern anrennas are often far less susceptible to interference from nearby aircraft and vehicles and so the restricted areas can be far smaller. Where it is beneficial to operations some States allow surveys to be carried out and permit any operations that do not cause the ILS signal to be disturbed. Consequently, distances and operational procedures quoted for one airport do not necessarily apply at another.
As others have pointed out, pilots can make practise Cat II/III approaches in conditions that do not require them. There seems to be a broad range of interpretations of what should happen when a pilot says he/she will make a Cat II/III autoland for practise - some pilots appear to assume that the ground equipment will be fully protected as would be the case in poor weather, others mention it for information only. One airport that I worked at said that I had to refuse the approach!!
caucatc, if your procedures do not specifically tell you what to do in this situation I suggest that you simply say "Roger, no low visibility procedures are in place" or something similar.
HTH.