It usually takes a bit over a day for the water to be absorbed, but the flooded ground is more than moist enough to need watering until the next flood irrigation water delivery. I currently have mushrooms growing in the middle of one of my lawns. However, the edges which are higher ground are dry and require additional watering.
I occasionally see mosquitos in small numbers, but they haven’t been much of an issue. The water does attract insects, and arachnids and reptiles that eat the insects.