Questions about example sentences with, and the definition and usage of "Humming"

A: is right. But. That was not the first thing that came to mind when I read the question.

There is a second context. For the second context, imagine an engine or motor. Could be gas or electric. The motor gives off sound. We call that a hum. As the motor speeds up or slows down the frequency of vibration changes. Thus the pitch of the hum goes up and down.

Now that you have this in mind. What is the purpose of the engine ? To get something done. Work or pleasure. The engine is working towards an objective. And so … when things are going well we say that things are humming along. Hard at work. No time for chit-chat.

Work at the factory is humming along.
The business for today is humming along.
Things are going well, no problems. Just humming along.