1. "I'd like to write to help understand how deep my understanding of the subject" -- You need to find the frequency you need to tune in so that your readers find you interesting. Things that require a deep understanding might not make a good story and appeal to the mass, and vice versa.
What I learned is that despite me doing an advanced degree, I only know very little that others don't: https://twitter.com/lolmythesis
To me, when I blog, I tell a story. When I write a paper, I tell how deep my understanding is on that subject. My knowledge of the subject matter is just a catalyst, not the cause, for me to tell my story.
Don't be shy about what you know, but I think the idea is you shouldn't assume that your readers are dumber than you unless you're Peter Norvig. But there are angles that you see things that are interesting to others.
2. No person I know or follow ever publish their homework to their blog and be successful. You need to add a whole narrative on top of that to be interesting, so I doubt anyone will have a problem with it. If you're worried about the legality, you're counting the eggs before they hatch.