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Grand Rapids, MI
How is the engine temperature? Is the gauge reading normally?
There is a possibility that the water pump is not circulating coolant, but you correct that if that was the case, you should see the engine temperature higher than normal. How is the temperature, is it lower than normal? It's possible that your thermostat may be stuck open and the coolant temperature is low, causing poor heater performance.
If the stability control is turned off, the light will stay on, but if you cannot turn it off, if the light stays on, then there is a fault in the system. You will need to connect an appropriate scanner to read the stored fault codes, and then diagnose the problem accordingly. These problems can be very technical and you should have a qualified technician address this issue.
While I'm not familiar with the exact location of your horn, what I can tell you is that many vehicles have two horns. One high, and one low frequency horns. When one of these fails the horn will sound very different than normal. Your Xterra should be under warranty still and I would suggest you have the dealer check it out.