Acer Laptop Failure

Yikes. Battery circuitry could still have been damaged. And since prismatic batteries have that wonderful habit of catching fire or exploding when over charged, might be safer to find a donor laptop on ebay.

These days the majority of the charging is done internally, so the power supply is only providing a constant voltage. Cheap ones may be poorly regulated and a little choppy, but any decent charging circuit will be able to smooth that out. A little more wear and tear, so it may charge slightly slower as a result, nothing too serious. Given the average lifespan of a laptop, not really something to be concerned with.

Laptop batteries are composed of Lithium that is self-oxidizing. When they reach a certain temperature, they will go into a thermal run away state and combust, even without access to oxygen. They can also simply be pierced and with exposure to oxygen or water (air tends to have both) they will also combust. That can mean just melting down, but typically there will be flame. Any signs of bloating and the battery should be disposed of immediately. Or at the least placed onto a temperature resistant or non-combustible surface, concrete is usually good.

The hard drive could have had bad sectors, if so, you are correct that it would attempt data recovery and move the data to a reliable part of the drive. Hard drives tend to have accelerometers and will know when they are falling and take immediate action to place the heads into the 'docked' state where no data is stored. If the drive was off, it would have already been in that state.