OK, go back to basics. The horn works by having a good +ve and -ve connection. Usually the -ve comes from being bolted to the bodywork but some horns have a permanent +ve connection and it's the earth lead to the horn button that triggers it. Either way the horn button turns it on.
Because it works better when something else is turned on means the original horn button isn't getting correct (full) power. If you've got a multimeter check the voltage at the horn button. Now do it with the fan turned on. If it's different follow the horn button wiring with the multimeter to find where the voltage loss is or rewire your horn button. If you haven't got a multimeter go out and buy one. They're cheap and a must have if you've got an old Golf. Check the earth lead too for voltage. Electrics are weird and you could be earthing through the wipers or fan.
Earth on the steering column is through the chassis where it's bolted to so the whole column is earthed.
Running on one cylinder and dying could be anything, even lack of petrol. Is the fuel pump making a sound? I suggest unplugging all the electrical connections in the engine bay and plugging them back in just in case you've got a bad connection. Do every connection, even the ones for the cooling system. You might need professional diagnosis on this one.
Cheers
Paul
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