There are ways to make the system do all of that with a single relay output. The simplest is to tie a DPDT relay to the on-board relay. Use one pole to short a "key" input zone. Use the other pole to trigger the garage door.
There are potential problems with this which you should consider before proceeding. If the panel happens to be disarmed when you push the button it will try to arm itself. Also, if the door is open and you push the button it will close the door.
One possibility is to assign an output to follow system arming status. By wiring the first relay's coil through the output of a "status" relay you can avoid arming or triggering the door if the system is disarmed. With a little ingenuity and a few relays you can simulate "IF .. THEN" logic. It is possible (but not necessarily advisable) to configure relays so that only under specific conditions will the keyfob trigger disarming and/or door operation.
Whatever you do, it would be wise to give careful consideration to the way it may affect the security of the system. For example, suppose make it very easy to disarm and unlock your home with a single push of one button. If that keyfob should fall into the wrong hands it would be like giving away the code and the house key. You have to select an appropriate degree of convenience vs. security for your home.
You can trigger a relay to activate based on several conditions, in this case you 'ld want to program and output function based on a "zone number".
First setup your relay in *79 menu mode.
Then you'll want to program an "output function" in the *80 menu mode. You' want to set it up like this:
Output Funct. # = 01 (assuming this is the first output function) Activated By: = 3 (zone number) Enter Zn No. = xx (requires 2-digit zone numbers)(this is the zone # your "off" key is programmed to -zone type 22-) Output Action = 1 (close for 2 seconds) Output Number = xx (device mapped in *79 Menu Mode)