Unless you have a short-circuit somewhere the battery is u/s
The battery is probably bad. As they get old they lose the power to recharge all the way. If you had a full charge you could still drive quite a while (with no head lights on) even with the alternator/generator dead, unless the gen/alt is shorting out which is rare.
A dead battery would not cause an engine to seize
Dead cell in battery, replace it.
no
The battery on the car you're jumping is too weak. Let the donor car charge the battery for about 10 minutes before you attempt to start it. If that does not work the battery has a dead cell and needs to be replaced.d
why would my starter wire burn, going from starter to battery
Because whoever told you that a low battery would cause hard steering is an idiot.
shooting it with a gun
Cause a no start situation.
Defective voltage regulator.
the battery could have a dead cell, this could cause it to not charge. Have the battery tested to be sure.
A raidator in need of a flush will not cause a battery drain.