This is an off-the-cuff answer, but to me, the distinction between "of" and"about" derives from what is meant by "opinion." "Opinions" can be a (a) statement of belief or position or (b) a feeling or attitude about a person or thing. so; What's your opinion "about" the proposed immigration legislation? Answer: [Here you would need an explanation of your position, ideas, conclusions.] What's your opinion "of" the proposed immigration legislation? Answer: it sucks.

Of would mean about, while on would mean regarding. It is so tiny that they are basically the same.

“of this” is much more common. In cases where someone says “on this” they could have said “of this” and it would be completely fine. If you are learning English my advice would be to just use “of this” all the time and make your life easy. As a native speaker even I am having difficulty defining the difference between them. All I could say is that I only hear “on this” when someone is referring to a document, situation, or multiple choice options that are right in front of them at that exact moment. When I imagine these situations the person is pointing directly to the thing in question. In all the scenarios I can imagine the “of this” works just as well.

It's a good question. One difference may be: "opinion of" - a judgment about someone or something: an opinion of sb/sth Her opinion of Adam changed after he'd helped her with her project. She has a high opinion of his abilities. I have a rather poor opinion of the sales manager. "opinion on" - a thought or belief about something or someone: What's your opinion about/on the matter? People tend to have strong opinions on capital punishment. He didn't express/give an opinion on the matter. More at https://dictionary.cambridge.org/us/dictionary/english/opinion

Probably, 'on this' could be asking about somebody's thoughts about a single matter while 'of this' would cover a wider topic. You can check out the sentences using 'opinion on' and 'opinion of' on the link Fraze.it