I think that a good first step in understanding a particular word and how it differs from some other words or words is to consult a dictionary.
So (and I know this is sort treading on your desire of the OP to put dictionary definitions aside, but I think it's necessary to make this point),
I might look up the word "know" and find a definition like "to perceive directly : have direct cognition of" from Meriam-Webster and think, "Hey, you know what, there seems to be something to that. Maybe knowing something has to do with some sort of direct perception or cognition of a thing."
And I might look up the word :"believe" and see "to think that something is true, correct, or real" from Cambridge and think, "Hmmm, so it seems like believing something has to do with thinking in your mind that they are true or real"
And I might look up "opinion" by just googling and find "a view or judgment formed about something, not necessarily based on fact or knowledge" and think, "It seems like opinions are not facts or knowledge, but instead are just a view or judgement. Maybe opinions are just like beliefs? Is there a subtle difference between opinion and belief?"
And after consulting the dictionary and thinking about it, then a good second step would be to find examples of how the words are used in sentences (which adds a level of context to assist interpretation).
In the case of opinion vs fact there is actually quite a bit written about that. So for example, if the sky is blue, we might know that by direct observation and we would believe it. And if the sky was covered with clouds, we might not know the sky behind the clouds is blue, but we might believe the sky behind the clouds is blue. And, in any case, we might have the opinion that a blue sky is good. And we could sum this up as:
"I know the sky is blue"
"I believe the sky behind the clouds is blue"
"In my opinion, a blue sky is good."
I found your description of how you use a dictionary interesting, @Ponder This, and I thank you for it. But two quick observations: First, as I understood the OP, it was not asking anyone to forego doing what you do, only to forgo quoting dictionaries in response to the OP. I could be wrong about that, though. I suspect @SalixIncendium would know more about his own OP that I do.
Second, my first wife was an associate editor of the Encyclopedia Britannica which, at the time, owned one of the Webster's dictionary companies. Some of their editors were friends of hers, so she learned how dictionaries are compiled. I could tell you if you have an interest in that sort of thing, but I'd rather know you had an interest before I risked my time talking about it.
Any way, thank you for your response.