As far as insurance and weather terminology, the areas that flood easily are referred to as "flood prone" or "low lying" areas. These are the areas where people need to keep an eye on when heavy rain and flood warnings are issued, as well as when rivers have reached flood level.
The low areas near a river that floods easily when water levels rise are call a "flood plain."
A place where a river rises is called the source or headwaters of the river. This is typically the point where the river begins, either from a spring, glacier, or other water source.
The surrounding land will become flooded.
Convection
A tall landform that rises to a peak is called a mountain.
Source
The formation in a cave that rises from the floor are called stalagmites
it is a bird called a Phoenix
Displacement
uplift, i think
Melted material that rises from the mantle is called magma. Once magma reaches the Earth's surface, it is then referred to as lava.
When water rises after you drop an object in it, it is called displacement. The water is displaced by the volume of the object that is submerged, causing the water level to rise.
Heat rises