Yes the buzzing noise is either a relay or the motor itself trying to start. But it is actually not the motor, but the condenser that fires the motor.
What the condenser does is store power in itself, and when the motor needs to start it discharges the stored power into the windings of the motor to give a shot in the britches. Without the extra boost the motor has too hard of a time getting started. Once going it requires less power, and this saves you money, and also saves the motor from having excess power going through its windings. This in turn makes the motor last much longer.
Yes you can leave the furnace switch off if you like. It wont hurt anything. You of course can not leave it on if the fan is not working. That could lead to a very bad situation.
As for changing the capacitor... Well that is something that I am reluctant to advise a novice DIYer to attempt. Mostly because the capacitors on these units can pack a serious kick if mishandled. They have been known to seriously injure people. One electrician I know said, "It is like being kicked by a horse smack dead in the chest."
So if you are not familiar with working around capacitors I think you would be safer to call a service person to do the repair. While he is there he can check the rest of the unit out also. I always recommend that they be serviced annually.
Thank you Karl. That would be great!
Good luck with your unit.
Best regards; The Home Smithy