Re: alarm
It's normal for the tach needle to stay where it was when the engine is shut off, ie whatever it reads @ idle. Turning the key to ON, engine OFF, should zero it. Like Bosunsmate said, unplug each to find the problem. If you stil have alarm with all unplugged, troubleshoot the wiring harness and cable to remote control box. Is your alarm inside the remote control box?
Running the engine with alarm sensors unplugged to test the system won't hurt it. The steady alarm is for overheat, but I've had a bad oil tank sender cause it.