is there a plugin to generate and offer completely static html files?
I agree with tobias - I haven't seen anything like that yet.
and is there a plugin that compress/optimize html data cached for the output?
In general, Typesetter will use several optimizations if they are enabled and supported by the webserver and browser - see A CMS for Fast Websites.
It will combine CSS and Javacript output by default but it will not agressively compress/minify it *.
For HTML compression: Although this depends a bit on the used themes and plugins, Typesetter's HTML output does not contain lots of whitespace or comments, so possible savings by compressing HTML would be below 10%.
* edit. almost all built-in JS libraries and plugins are minified in the stable/production versions of Typesetter.