Yeah, that's how it should work, but that doesn't mean it necessarily will work. Your machine's showing some pretty bizarre symptoms so certainly try adjusting the volume, but I don't know if it'll be recognised. Alternatively,
reset the PRAM and see if that gets your volume unmuted. Having said that, I thin we might have bigger things to worry about than the startup chime.
Technically yes, but I wouldn't know where to start. Do you have any idea what changes you've made to the system that might have brought this about? To be honest, I think your best bet right now is to do an
Archive & Install, so how hard would it be to get your discs back from home?
In the meantime, is there another Mac (
Target Disk Mode) or an external drive with OSX on it that you could boot from to back your data up?