first I would see if there is hot anywhere. if not the problem is with your water heater. if its electric check your breaker or fuse box. if gas call your friendly plumber
the shower and bath water comes from two different places so their is two different pipes. Get the shower pipe checked out by a plummer and they cause fix the pipe.
yes you are even though you are not in the shower you are still wasting water
means you are running out of hot water
The difference between a shower and a tub is the shower tends to enclosed with water that comes out of a shower head above while a tub has a faucet that pours into a large basin.
Remove the shower head and clean out anything that might be blocking it, such as hair or debris. Replace the shower head and turn on the water; the water should be running.
So If the main hole blocks the water do not get overflow through basin.
There is a drain at the bottom so the basin can be emptied, and there is an opening (another drain) near the top so that if someone leaves the water running, the water will never reach the top of the basin and overflow.
More "VOLUME" flowing from the tub spout then the shower head as the shower head has a flow restrictor
The valve is not be diverting all the water. This valve may need to be replaced.
You need to do a leak test on the tub and shower. To ch'k the drain fill tub about 1/2 full without running the tub faucet next plug shower head and tub spout turn water on this will ch'k faucet Next run water on shower doors this is where the majority of leaks are found water running out and down the corner of the unit If tiled also ch'k tile grout.
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Remove the shower head and clean out anything that might be blocking it, such as hair or debris. Replace the shower head and turn on the water; the water should be running.