calibre conversions will always flatten the CSS. You
will end up with a finely blended (think food processor) ebook whenever you use calibre to convert a book.
This is done in order to ensure consistency, as calibre's conversion pipelines do things to fix rendering on a variety of devices. To an end user who will not (typically) need to modify the code, this should not be a problem. If it's a problem anyway, you might want to use kindlegen instead.
Question: Does the ebook look wrong on a device after conversion? If so, you *might* want to submit a bug report. If not, you are complaining about a non-issue.
Although as theducks said, calibre should not be misspelling it's own name! That leads me to suspect something is missing here...
As for downgrading tags from <h2> --> <p>, if you are truly converting to MOBI (AZW doesn't exist) as opposed to AZW3, that may be your problem. I am pretty sure the mobipocket7 format (popularly known as
MOBI, though Amazon muddies the waters by giving it the .azw extension) does not support such bleeding-edge HTML technology as header tags.

It also doesn't support CSS.
That's why they invented AZW3 (
KF8) -- to fix those problems. Why are you using ancient, inefficient, primitive, barebones formats?/