Either there is a short on the horn circuit, or it's going bad. Check for voltage at the heater. If none on low, check the blower resistor. If none on high, swap the blower relay.
If the parking brake is not seated or the switch is broke, the light will stay on.
Are you running amps, running lights, etc? The harder the alternator works, the hotter it will get. Be sure you are not overloading it. Borrow an amprobe and run everything with the probe on it to see what you're drawing.
You have to stand for something, or you'll fall for anything.
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