They were going to be based at Ohakea, which is close to two small settlements but otherwise essentially rural.
I'm still puzzled by the hush kit reference, since they are simply not a thing for F-16s, or any other combat aircraft. Nobody I have spoken to or seen discussing the F-16 acquisition...
Your dates aren't quite right. The F-16 lease cancellation announcement was in March 2000, the decision to disband the ACW in May 2000, and the actual disbandment in December 2001. A number of Skyhawks and Macchis were kept airworthy for demonstration and currency flights through the mid-2000's.
More that an incoming government was fundamentally ideologically opposed to the deal rather than any ignorance. It's own commissioned report into it recommended a reduced buy rather than outright cancellation.
It was in the mix as a potential A-4 replacement prior to the Kahu decision in 1983-84, but without a significant order from other customers it was never a serious prospect for the RNZAF.
More likely they get LAVs, but in reduced numbers. There are a lot of stories, possibly apocryphal, about the number of LAVs acquired vs how much were actually required.
The Skyhawks regularly deployed to Australia and Southeast Asia, with one squadron fulltime based in Australia from 1991 to 2001 - the homeland defense mission wasn't as big a thing as training to operate with allies overseas. The F-16's would have continued this role.
Unlikely, for cost and...
Not quite
Draken International purchased 8 to use for aggressor work when they bought half of the Skyhawk fleet, and they have gone on to be employed on fleet support work in France. The rest went to museums in NZ, one remains at Ohakea in private hands.
Idle speculation, but they may also have been impractically expensive to convert, as the EC-121's were factory built rather than conversions. I'm not sure of the economics of this either way, but it would be a significant factor.