Not unless the cables were hooked up in reverse.
Disconnect battery from vehicle - if this still happens battery is probably shorted internally and requires replacement
Depending on the age of the vehicle you probably have shorted or grounded the electrical system causing fuse(s) to blow. Question was kind of broad may want to be more specific
Yes. If the alternator is dead and you drive the vehicle, all the power is coming from the battery and it will eventually drain completely. Also, if a diode is shorted inside the alternator, that can drain a battery.
Dead cell in the battery itself which requires you replace the battery. Can also be any light on the vehicle that is on pulling power from the battery. It can also be a relay that is stuck closed.
Nothing, the battery did it's only job by cranking the vehicle. Now it is up to the alternator to keep all electrical working while the car is in operation.
The battery gauge in a vehicle will move when you use your power mirrors as your causing a small drain on the battery & lowering the voltage slightly. The effect is normally only really visible when the engine is not running.
In order to get the battery out of a Mercedes e550, you should consult a professional mechanic who knows exactly how to do this without causing any permanent damage to your vehicle.
By running the engine on the vehicle or by connecting the battery to a 12 volt battery charger.
a car battery made for that vehicle
Check the fuses. By hooking it up backwards, you may have blown many fuses, and/or completely damaged the vehicle wiring system, and/or shorted out the starter motor.
The only method of disarming the security system is thru the door locks, if it does not disarm; this will entail a fault in the security system. First, the vehicle battery will have to be tested, a low, or shorted battery can trigger the security as well. If the battery is good, the sytem will need electrical diagnosis, which I recommend be done at the dealer, since they are more familiar with this vehicle's security system, than most independent facilities are.
The alternator may be putting out charging current, but the battery may be old enough that it is shorted out internally and is not accepting the charge. It's a simple enough thing to check out - take vehicle to a shop (or auto parts dealer) who can put a meter on it and check it.