1. It may or may not be a bad alternator. There isn;t enough information to decide.
2. The squeaking noise from the engien compartment could be many things, including a slipping accessory belt. That would at least contribute to poor charging and possibly be the cause of all the problems.
3. Of course you can change the alternator yourself. It will take some time, patience, and a few tools. It's not that difficult.
If you decide you want to replace the alternator, you'll have to remove the accessory belt first. Make sure the tensioner has adequate spring tension, the belt is not worn or cracked, and when the belt is removed, make sure the alternator spins freely.