A "fact" must be true. That's a tough issue since we disagree on objective truth.
A "factual statement" or an "empirical statement" must be a statement that only aims to describe the nature of reality, with no value-laden baggage.
To me, the surest sign of an "opinion" is when someone expresses what should be or ought to be, what people should do, if a particular state of affairs is bad or sad or cruel or good, etc.
In common usage, we use "opinion" to mean this and also an uninformed factual statement that is based on little evidence. The latter use is purely pejorative and heavily subjective.
In my view, an opinion that evinces a lack of compassion or empathy, a lack of proper thought or deep relation, or a lack of passion about the issue is likely to be a bad one. I believe that, if we don't really care enough about an issue to really at least consider it from a few different angles, we really have no pressing need to share it.
Moreover, I believe that we all must be a lot better at indicating the strength of our opinions and our estimation of their importance to us. For example: When I talk about the existence of God, I say that I believe in a pantheist God because of my life experiences, but do not have any evidence for that assertion and actually do not find it all that important to my life. To me, it was the experiences gaining a broader sense of consciousness, joy and awareness that mattered, not one of the specific conclusions I drew.
The popularity of an opinion is totally moot to its soundness. The reason why we discuss the percentage of experts in a field who believe X versus the general public is because there is an implicit argument beyond the popularity: "The people who actually did the work, read the arguments, ran the models, they believe this. The general public is virtually by definition not experts in the field, and thus are likely to be incompetent at making the judgment in question". However, in practice, we do see minorities that have opinions tend to be more likely to be people who have to shield themselves from logic contrary to their preferred view; who acquired that view only as a result of being born with it or some encounter (like a Scientology encounter) where they got drawn into a belief system for reasons not very related to a truly sound and compelling argument drawing equally from pathos, logos and ethos.
A "judgment" has, again, two distinct meanings: An opinion with some kind of additional implicit moral sanction or forgiveness, some kind of excoriation or applause; and an assessment of complex evidence combining an executive-level overview with one's gut instinct.
An opinion is certainly related to knowledge, experience, education, intelligence, emotional intelligence, self-awareness, empathy, etc. etc. Our opinions are based on our worldview and who we are.
In my view, there's an additional rub: Vantage points. How one looks at an issue can be dependent on who or where one is. That's true in physics with relativity and it's true in life. If we say "Rising housing prices are good for the economy", for example, that statement may be defensible, but they're not good for people looking to buy houses right now. Different stakeholders can have directly opposed needs. When discussing an "opinion", then, it's cognizant to be aware of what perspective one is implicitly using for that opinion: If one is speaking in one's capacity as a theologian, scientist, scholar, Buddhist, martial artist, sociologist, or economist; if one is taking a big-level view or a small-level view. Where a lot of opinions become contentious is when a person is incapable of ever adopting a different vantage point: A MRA concerned about false rape accusations being unable to drop that political commitment to actually be kind to a victim; a feminist concerned about abuse of women being unable to recognize that her male friend may be in serious trouble. We are altogether too good at letting real people fall into the cracks of our ideologies.
My answer to this topic is of course 100% an opinion. Still, I think most people could agree with my general layout here.