fuel pump kill relay

With a normally closed setup you should be able to start the car when the (-) when armed wire is disconnected from the relay regardless of the state of the alarm - verify that you can do this first.

It sounds like you have mixed up the 87A and the 87 pins of the relay - make sure you are using a normally closed contact pin (ie 87A) to wire the relay to the car.

if your unit sends ground when you disarm insted when you arm, wire it like so. but, your unit might be programmable for how the wire sends out a ground

85 - ignition