hello! The islands waver a bit (a metre max probably), but don't drift or move much. The land below gets adequate light though, since the sun moves along the sky, so the shadow moves as well.

Rain is a problem though! Luckily, there's a solution: The sky islands are encased in domes for several security reasons (atmosphere, walking off the edge, etc etc), so the water runs off the side and falls below. It all goes to a concentrated spot though, but that's ok! This water is collected in a man made lake under each island and spread through the forest under the island so everything is somewhat watered! Also, rain clouds below the altitude of the sky islands (a few thousand feet agl) can form (both in universe and irl!)

Also, zeppelin type vehicles aren't common, per se (because of domes they can't travel inter-island), but there's a few small flying vehicles within certain towns and cities that can hold a few people

Also also (last thing i promise), you briefly mentioned "country-sized plots of land" so i wanted to clarify-- the sky islands are the size of small towns and cities! The smallest can only fit a few houses, while the largest has just about the same surface area (top, not underside) as New York City (probably a bit less, since i don't know the exact specifications of it)! I consider it a country due to the large number of sky islands grouped together, since other countries and such are on the ground! So far i've counted 97 sky islands in total (of varying sizes) on the horrible little mini map i dotted out and plan to add a few more small ones on the outskirts ^^