Yes
it depends on the type of bowl...
No, it can't have the same thermal energy. The hot water loses energy to the surroundings. Cold is an absence of energy, as energy is removed the water becomes cold.
Since hot water is less dense that cold air the hot water will rise and the cold would sink then it keeps doing this in a circular motion 'till the thermal energy reaches to thermal equilibrium.
The energy content of still water isolated from external energy sources is generally thermal energy, and "cold" is in actuality the absence of heat. Thus the colder the water is, the less thermal energy it contains.
No, the thermal energy of any object is a multiple of its temperature (absolute), the specific heat of the material it is made of, and the mass of the material. So obviously a large pot contains more energy than a small one.
Yes
Yes, the more substance you have, the slower the temperature change.
That would be convection. Thermal diffusion of energy from a high concentration to a low concentration. Depending on the application or context, the loss of energy can be reffered to as entropy as well.
Thermal energy is the internal energy of a system in thermodynamic equilibrium by virtue of its temperature. A hot body has more thermal energy than a similar cold body, but a large tub of cold water may have more thermal energy than a cup of boiling water. Thermal energy can be transferred from one body, usually hotter, to a second body, usually colder, in three ways: conduction , convection, and radiation. Insulator
thermal energy is energy in the form of heat.
Something is conducting thermal energy if it is hot or cold to touch. Heat is thermal energy and heat can be felt by either the feeling of cold, or hot.
Thermal energy can power up many things maybe billions sometimes thermal energy is powering up heaters (most of the time)