1994 Honda Accord Hmmmm sound from alternator area

It is possible that the problems are related, if the internal part of the alternator is bad. The humming you hear is probably from the bad bearing. It is possible it is the alternator bearing, but it can also be any one of the pulleys.

The jump starting is due to your battery not holding the charge, probably due to a weak battery or your faulty alternator.

This is what I would do. Take the battery to an auto parts store (Autozone, CSK/O'Reilly, Napa) and have the fully charged the battery. Once it is fully charge, load test it. Once that happens, re-install the battery take the the vehicle to them so they can test the entire electrical system. Then you can find out exactly what needs replacing.