The tap water prevents the battery from holding a full charge because the plates usually sulfate quickly. That is why all demands are burdened on the alternator and the battery does not fulfill its reserve current function to the full.
The alternator will also have a very tough life if the ground connections are not good, Ideally a good ground connection should be a direct to the transmission case and branching off to the body - the branching maybe just one or even have more than one connections.
Just to test, take a jumper cable and connect the negative terminal to the cylinder head lifting hook, then try the headlamps dimming thing, you may find your culprit