Helpful tips:
1. ADE is very picky about CSS files. If it encounters anything it doesn't like (including
some valid CSS3 @media and @page rules), it throws out the entire CSS file.
2. For a long list of known EPUB reader bugs and workarounds, see the
EPUB page on the MobileRead Wiki. Several of the problems you've encountered can probably be fixed with the workarounds in that list, including (in all likelihood) the header formatting issues.
3. Test content on your computer first in Safari (or possibly Chrome). 99% of the time, an Android EPUB reader is going to be based on WebKit, so Safari is likely to be the closest match to that in terms of rendering behavior, followed by Chrome coming in a close second.