How would I create an arbitrary mesh during runtime, copying the shape of the terrain underneath?

I'm currently playing around with a city building game, and I want the player to be able to make farms, by dropping x amount of points to create a polygon, confirm the shape, and build a farming field in that shape.

The terrain can go up and down, so I would prefer for the farm to "fall down" on the terrain, instead of it being a plane. It should also check if it's building in a legal spot (i.e. no houses, preferably no steep drops, e.t.c.) I do use nav meshes for navigation - and I think the walkable parts of the nav mesh should be pretty good for determining legal placement.

Additionally, I would like the player to be able to select the farm again, and change some options, and preferably also the shape.

Finally, I want to be able to revert the farm land back to normal grass.

An idea I have at the moment is basically just to make a custom mesh, "copying" the underlying terrain - but I don't know of or how that's possible. If not, how would I approach this?