The non breaking spaces are being preserved. They're just encoded as UTF-8 characters instead of HTML entities.
The next release of calibre will have a --level3-toc option.
The calibre viewer does not support CSS based page breaks. This is not a problem if you generate EPUBs using calibre, since it will automatically split them up on page breaks.
All the epubcheck warnings you see can be ignored.
The bug about empty paragraphs is not really a bug, since representing empty paragraphs as <p/> is perfectly legal HTML.