I'm glad I'm not the only one who doesn't agree with the headering systems in the skins. They are something that many of our client - mostly new to Moodle - all come back to us about time and again. In cases where we are designing a skin for them, we tend to not even show the standard page headers and just hard code our own, because that makes more sense.
I've never seen the need for having the same text over and over and over - and many of my clients agree. Either have a header, or rely on a working breadcrumb and educate users to look there, or have a topic header that makes sense (which only works if your topic names are short, which for me they often are not).
Breadcrumb length becomes an issue in items 9 and 10, though at least Moodle has the sense to ellipsis long topic or course names. In one case, a client asked us to remove all the extra levels from the breadcrumb and just have a "home > course > topic" and nothing more, and not activity or action at all. We still hit the problem that the page header was 2 lines long plus an extra line for the topic name because their course names were that long. That looks incredibly messy.
In the skins I'm now building, I've been putting options into the skin settings pages to option what appears, to over-ride the built in page headings and be able to turn them off, because they just don't make a lot of sense. I'm glad you went to the trouble of documenting all this because like you I'd done my head in trying to understand what gets drawn where. I'll be marking this thread as a nice reference.