No
The battery is dead.
get a new laptop
The laptop will turn off when it is unplugged from the AC adapter
it does from experience....
Borrow an exact battery and test - original battery is likely bad.
Laptop batteries generally have a lifespan of 3-4 years depending on usage.
No.
the computer will shut off entirely
Not unless it is plugged into a wall outlet.
Turn down the brightness settings
Either a dead battery - or a faulty power supply.
Dead battery or corroded battery connections.