A real gunshot actually is not that easy to identify. It sounds more like a firework (in my experience) than the gunshot sound effect we hear in movies. People will still call the police, hopefully, but I would not assume people will identify it correctly.
Kevlar can be treated to be stab resistant. It's not as good as a rigid plate but it's much better than a "really heavy sweater."
This is correct. Just as important to note, though, is that armor piercing is comparatively good at piercing because the standard self-defense bullet (for non-military use) is a hollow point, which is designed to flatten and expand upon impact, transferring more energy to the target. This is more effective against flesh, but less so against a vest, which tries to disperse the energy across a wider area. The hollow point works into this tendency, while the "armor piercing" bullet fights against it.
The person you quote specified an already drawn knife. The Tueller Drill puts the threat range at about 21 feet for holstered gun versus a drawn knife ...which is pretty scary.