It is perfectly reasonable to place an image with other text within a heading, however, it would be stupid to place an image on its own within heading tags.
Headings are block-level elements so if you want to align an image with the text of a heading (which is entirely reasonable) the only sensible way to do this is by placing it within the heading.
An h6 above an h1 is improper code syntax
Again, only a code-nazi would believe this...
Firstly, the ultimate heading of a page is the title, therefore you may reasonably have as many H1 headings as you wish and undoubtedly you could have an H6 above the second H1.
Secondly, it is perfectly reasonable to place an H3 within the range of an H1, etc. therefore, following the logic from above, it is reasonable to use an H2-H6 as the first heading and use an H1 below it.
Doubtless someone will disagree, so consider this...
Let's say I have a website about spare parts and I want to place common generic parts are the top of the page. Each of these parts might reasonably be given an H2. Then, below the generic parts I might want to list parts by manufacturer. The manufacturer names might reasonably be given H1 so that the parts themselves are given H2 (just like their generic counterparts).
Use H1-H6 sensibly for the content of your page and ignore idiots who tell you that this or that is wrong.