Those top level domains are strictly regulated and only recognised government or educational institutes can register them.
The site owners cannot be anything but government / education.
The sites may have content copied from other places and are pretty much guaranteed to have links to other web sites, if that's what you mean, but the sites themselves must be legit.
Yes, being a gov/edu domain almost always can be used as a trustworthy source. Some contain primary source-information, but I assume most will be secondary sources.
Yes, as can many websites.
They are, in fact, and excellent source for primary sources.
Yes, though their content is restricted to governmental work (.gov) and educational work (.edu), obviously. You couldn't have MySpace on a .edu domain, for instance.