I love this movie so much ! Some fun facts about it : you were right about the improvisation, the dialogues of the movie are totally improvised. And about Stu, he's not played by an actor but by an old college friend of Taika Waititi and Jemaine Clement who really was a tech guy. No one told him how much he would be in the movie and until the premiere, he thought he would just be in a scene or two.
The two cops were so funny that they got their own show, “Wellington paranormal”, that I recommend, and the movie itself has its own show, not with the same actors but honestly as funny.