Google-drive – On Google Drive is there a way to connect Adobe Reader using “Connect more apps”

There is no mention of the supported version number on either the Google Docs Viewer tool page or the View files in Google Docs page from Docs Help.

I don't know if it is possible to give a complete answer to your question but my best guess is that there is not any officially supported version, but rather that the team tries to keep the tool as up-to-date as possible and to support as many features of the latest version of PDF as possible.

Since the viewer is provided as a web service, Google doesn't necessarily have to think about supported versions in the traditional way. They may be closely monitoring usage and as they receive error reports during rendering of documents from the web service, they may be working to resolve those problems so that the percentage of successful views is as high as possible. After all, in my experience there have always been vendors who "supported" a particular version of PDF but which did not successfully render particular documents due to bugs in the rendering engine - but the existence of bugs didn't change the officially supported version number.

When you have an HTML file in Google Drive and ask to open it with Google Docs, there's no 'convert' option AFAICT and you get a 'view source' sort of view instead of seeing it rendered.

If you have the HTML file saved locally and you upload from the Google Docs page itself, there is a 'convert' option in the upload dialog, and that will produce a rendered version of the page. In my limited experience with that conversion step (importing some HTML produced by the ASCIIDoc formatter), the rendered HTML didn't look very good -- it came out with an awful-looking font and lost some formatting from the original HTML.

The top-rated Google search results for importing HTML into Google Docs all seem to assume you're importing HTML data into a spreadsheet.

So while it seems to be possible to get some kind of rendered HTML by going through one specific path, this doesn't appear to be a high priority for Google Docs.