No problem with the doc type. You are getting some errors because the code is not to XHTML 1.0 Standards. You might try Strict: Doc Types.
There are no "table tags for CSS". You can use CSS with your table tags, but tables have been out since 1990s for use as page layouts. Should be used for tabular data when needed. CSS is for your page presentation and is the best way to go to make a nice page layout.
Some links for tutorials:
As for CSS with tables. Instead of doing this:
<table width="100%" height="100%" border="0" align="center" cellpadding="1">
You could do this:
<table style="width:100%; height:100%; border:0; text-align:center; padding:1px;" summary="">
and similarly with the other tags you have including the divs. Would be better to set up an external CSS stylesheet and use class/selectors where needed to style your pages instead of the inline styling above. It's a beginning.