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Should remove the battery to charge, at the very least disconnect it from the car!
I am guessing the horn is related to the alarm system. If it looks like a snail, it doesnt have a battery. If it is squared off box like 'thing' it will be a battery back up system (BBUS), which are prone to failure. (fitted if you have factoory Xenon headlights).
To test the alarm, the simplest method would be to open the bonnet, press the sensor button (rubber cone shaped at the front), then whilst holding it down, lock with the remote. Keep the sensor button held for about 15 seconds, then release. If the siren doesnt sound, and the indicators flash, it means your BBUS has failed. Since they are plentiful on eBay for around £10-15 (search BMW e46 e39 alarm
EXAMPLE) and generally reliable in BMWs and Binis, I would just replace (a wiring plug and a nut if I recall).
If it is the snail type, I would still test, and assume, if it works correctly, it to be something related to fitting the charger to the car's wiring system.