Bad stuff
Yes, that is the purpose of a trickle charger. Just make sure it is an automatic charger that comes on when needed and then stops charging when the battery is fully charged. You can leave it on a battery for years if need be.
Yes, it is generally safe to leave a battery charger connected for an extended period of time as long as it is a smart charger that automatically stops charging once the battery is fully charged. Overcharging can damage the battery, so using a smart charger is recommended for long-term charging.
You die.
When it stops working
Most mobile chargers aren't really chargers, but rather a power source. The electronics that monitors the charging and stops it when the battery is full is all in the cell phone. IF you hook the cell "charger" straight up to a battery you run the risk of disastrous overcharging.
You die =)
If that happens, the body will starve to death.
You would die..
everybody dies
Get a new one.
you get a new charger
What happens when a transmission control solenoid not working