The style rules in the sgc-# classes are actually in your document already as contents of the style attribute on the XHTML elements, the so-called "inline styles". Since these are deprecated in the specs and also difficult to maintain due to duplication, Sigil (actually embedded HTML Tidy) pulls them out into separate CSS classes with these sgc-# names. The document renders the same.
Sigil basically doesn't touch separate CSS files at all. It's just these inline styles in the XHTML itself that are pulled into a <style> tag (again, it renders the same, this is just easier to maintain and also conforms to the spec).
For the epubcheck errors you'll have to post the epub file. Can't help you blind.
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