There‘s a great video on that topic by Matt Parker (Standupmaths) which I‘d wholeheartedly recommend.
TLDW: No, terrain elevation isn‘t generally taken into account when calculating a country‘s surface area, though the actual method differs slightly from country to country. Switzerland would be around 7% bigger, if its mountains were to be taken into account.
(source)
Not a map, but at least some more data from some other countries. The own car is unfortunately the most used mode of transport for commuting in every surveyed country, but the US seem to be especially far behind when it comes to alternatives.