so, how often do the mk1 and mk2 reveal tiles? is it one tile per cycle? do I need to put down a bunch of mk2s to enrich a field before mining?

It's one tile and one upgrade level per cycle. Mining/prospecting can be done in any order (upgrade adds the remaining ore to the upgrade ore amount), but mining upgraded ores is slower. A single MK2 prospector can generally prospect the ore faster than the miners can mine it.

How do these even work? Do I have to deplete an ore vein to make it work?