The answers to your questions are never and yes respectively.
The original HTML5 spec at the WHATWG is now simply an HTML spec. New features are added all the time, old features are updated according to what ends up getting implemented. It will never be finished, instead it will be an evolving document and a place of convergence for browser implementations.
CSS2.1 didn't get implemented completely in any browser until recently, in fact it didn't even get published as a standard until June 2011 so it was impossible for any browser to claim full support. I'll bet (though I could be wrong) you were happy to use CSS2.1 features before then, you just used the features which worked and avoided the features which didn't (hence the proliferation of float based layout techniques over the often more suitable inline-block or table-row/table-cell available in CSS2.1 - float could be made to work cross browser).
Some HTML5 features, like drag and drop or XMLHTTPRequest (ie. Ajax, no longer strictly part of the HTML5 spec itself) have worked in browsers as far back as IE5.5. There's no point not using them if they'll make your application easier to write just because other features don't work cross browser or aren't yet implemented.
In the WHATWG version of the spec each feature is annotated with some information about the maturity of it and current browser implementations. You can also use resources like Can I Use to determine what sort of coverage among web users a particular technology has.