As for the technical side that seemed to be left out in that article... The operating range is 10 to 20 nm. As soon as an a/c is found within range it will be databased and continuously tracked.
Tracking is done by ATCRBS replies, mode C/S. Altitude of an intruder comes from the altitude encoding, the distance from the timing as per usual for secondary radars and the angle from using a directional antenna.
TA/RAs are generated based on a value called the tau value. From two subsequent distance measurements a closing speed is calculated. This and the distance gives a time to impact value, namely the tau. When this goes below a certain number of seconds a TA is generated. Under a second threshold, an RA. These thresholds vary depending on altitude AGL.
Alt TA tau RA tau
0-500 20 inhibited
500-2500 35 20
...
20000+ 48 35
I hope that answered the rest of your questions.
IIRC, the level of nuisance alerts is about 2/3rds of the alerts which is quite low for such a simple system. I plowed through a paper or two on conflict detection in ATC systems and it can get quite a lot more complicated without decreasing the nuisance alert level all that much it seems. ATC have some pretty neat systems in operation to show potential conflicts far ahead in time and it's getting better all the time... Add ADS-B and we'll be able to cram so many planes into the skies that they will darken...
Cheers,
/ft