Most of your problems are caused by differences between html and xhtml - epub uses xhtml. The easiest way to convert .doc files is to use Atlantis Word Processor, but it's not free. Alternative free solutions are to use the Open Office plugin that's listed in the sticky or to import the html into Sigil.
1) This is a bug in epubcheck itself, but to resolve it just edit the metadata value for the date entry in the opf file so it fits the YYYY[-MM[-DD]] format.
2) 3) 4) Just remove the offending attributes from the xhtml.
5) Hard to say without seeing the file, but this is commonly caused by p tags being nested. Check the structure of the code.
6) Name attributes are deprecated in <a> tags, use id instead.