An error occurred while saving the commentJakub Štěrba commented
I would like to have also option to either show all labels if they do not overlap or none. This is essential to have good looking charts on different screen sizes. While data labels may fit on desktop, it may be better to hide them on smaller screen because of overlapping. There is no point to show only some of them in case of many data points in my opinion except for showing for example only minimum and maximum values.
You can create Trellis charts in Highcharts by adding multiple charts side-by-side or underneath each other, for example inside a table or floating divs. See http://jsfiddle.net/highcharts/VqruM/.
Black Label kindly shared their grouped X-axis plugin: https://github.com/blacklabel/grouped_categories