Not entirely sure, but you could probably find some (probably inaccurate) descriptions of how their armies were fed in Herodotus's Histories.

Not sure what you mean by "land transport", but remember that the Achaemenids had already acquired much territory in neighboring regions. There were likely already garrisons of soldiers in places like the Ionian cities, and let us not forget that many of the soldiers serving under the Achaemenid kings were from a variety of places including many mercenaries from Greek cities themselves. They wouldn't have necessarily all come from Persia, and would not have a need to travel particularly far.

Phoenician mariners famously comprised most of the Persian fleet, so this is a likely answer to your last question and further evidence that it wasn't a matter of a Persian king deciding to invade Greece and rounding up some fellas from a barracks near Persepolis and marching thousands of miles in one shot. The empire was famous for its vast network of roads and "pony express" communication system, after all.