The detectives see that Gabby has received a false text and instead of using the computer to send her another right away telling her to disregard or calling her right then, they leave and then later call her while in their vehicle, just missing her.
When they are trying to figure out the suspect's true identity, a character says they could check the interrogation room for prints. Det. Dawson had already arrested the suspect for spitting on him, so they would have his fingerprints by that point.
When her elevator first gets stuck, Gabby presses a few buttons, including the door close button. While some elevators have door close buttons that are empty buttons (not connected to anything) and some have active door close buttons, it is unlikely that telling an elevator to close the door would either open it (so Gabby could get out) or otherwise assist her in any way.