A:
It's a very strange way to say it.
I would never write like this personally, even in an academic writing.
I would write: ".. being persuaded that it is often beneficially productive to the professor, and to others that are within his sphere of action."
"to do good" can mean "good" in the "noun" sense, as a good deed or action. But "productive of good" sounds strange.
This is why we distinguish between the answer to the question, "How are you?"
"I'm doing well" is correct.
"I'm doing good" technically means you are doing a public service, something admirable, or something beneficial to society.