Yes, search engines will go through your html code and make judgements on your site based on the code it just crawled. Specific html elements will also make you more liked by the search engine.

Your misunderstanding how server side CMS short-codes work.

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Those themes have a lot of comments in the code that make them easily identifiable, it that is what you are worried about.

Of course Google reads the generated page HTML, but I guess nobody here is confused about that.

WordPress themes are usually easy to identify from the HTML. People are lazy, and don't want to rename theme directories so if you take a look at the HTML source the theme name is usually just sitting there. Some themes are fairly minimal in their markup, but others have very easily identifiable structures and naming conventions. Compare StudioPress Genesis (sort-of stealthy) to iThemes Builder for example.

Theme could be a part of a footprint, but the most popular ones are widely used. You'd need much more than theme to identify a network.

Google can see your HTML code that is the only reason you are write the Meta description and title and other on-page tactics.