Yes
No, they each need their own breaker of the right amp. Neither of them would cause the breaker to trip if there was a problem.
Because hot water heater breaker has tripped, or hot water heater has failed.
turn off your water
There is no way of telling from here. It will be a double breaker, most boxes will have 3 doubles. One for the stove, one for the AC and one for the water heater. Process of elimination should tell you which is for the heater.
The wattage of the water tank is needed to size the breaker and the wire to feed the tank.
YES!!
The best way to determine which circuit breaker is for the water heater is with a voltage meter, It is suppose to be only one circuit breaker, but in a faulty application it could be two breakers
Sometimes the top heating element gasket can become faulty and cause the lower element to leak and this will cause moisture to build up and short out the lower element.
yes, the breaker just controls the heating elements
If the tub is not getting hot water the issue is probably with the hot water heater. The hot water heater may have tripped a breaker or the pilot light went out.
Only if the hot water breaker is turned off.
Could be a bad heating element or a bad breaker, either of which can be fixed. The only reason to replace a water heater is if it is leaking. Anything else can be fixed cheaper.