I've read the novel and saw part of the movie.
1.Their refusal to acknowledge him is a demonstration of how surreal and out of touch the 80s yuppies were.
They were so locked in their rich little world that nothing could shake them into reality. Bate was mocking them.
2.He wants to get caught because of his ego. Serial killers end up leaving clues, because subconsciously they need validation.
They want all the credit for their well planned crimes. Again, it boils down to control. By terrorizing whole communities, they feel powerful.
3.He let his secretary go because again, serial killers usually murder to gain a feeling of power over others.
As his secretary, he already had her bending to his will.