Norman
I'm presuming your question is a serious one. This lead plugged into your alternator is for the charge circuit to your battery. The alternator outputs current in a regulated fashion [as in via a regulator, which is integral, inside our alternator] to the battery. In this way it keeps it topped up, and not overcharged.
With that plug out, your battery would be drained of current every time you switched on lights, fans, etc.
This in turn would cause the alarm to go off once voltage was very low [failsafe anti-tampering circuit cuts in], and the other problems you describe.
It was probably left off by mistake by whoever put in your new battery, and that by your description was the alarm people.
Good news is all should be OK with it plugged in, UNLESS the regulator in your alternator is faulty. I expect it's OK though.
Joe
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