There are many varietals of rice. Most do not grow in marsh land. Farmers often do flood the fields at the beginning of a rice growing season in order to drown out any competing plants. Flooding is not necessary though. Rice will grow with normal irrigation.
Yes. Rice tolerated flooding better than weeds so it is used as a cheap and easy weed control. Also some places grow fish alongside rice in the same land, getting some extra pest control and fertilizer for free.
edit: Looked it up - Rice has the highest number of calories per square metre of farmland, just that it requires marshy/swamp land to grow.