Most tubs do not have a shut off in the supply lines to it. You have to shut the main off where it comes into the house.
The valves were installed improperly.
Remove the handle, turn off the water with a wrench and reatache the handle in the correct position. Good Luck
Depending on which type it is, it either need a new washer or seat in the valve. The washer is a flat rubber disk that seals when you turn the faucet off and the seat is a small rubber cup that does the same thing.
The mains water has probably been turned off and turning on the tub has drained the tank.
A Roman tub faucet does have good water pressure because it is made to do that. How good this is depends on how other brands perform in this area.
It depends on the make of the faucets.
A tub faucet acts as a shower and can be used to bath in the bath tub. It is a pressure valve which makes the flow of water through it constant and gives a nice shower.
Maybe the kitchen is further away and on smaller pipe.
If the faucet contains the re-direction valve (closes off the water from the faucet and redirects the water to the shower head) you need to rotate the faucet counter clock wise to unscrew it from the plumbing and replace it with a new one. Take the old one to your local box store and they can match it up for you.
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.
yes it is other wise u would have a huge mess.
If the tub has a shower as well, the pipe from the faucet to the shower head could be leaking. You might also check the tube that comes OUT and fills the tub. It could be leaking back at the valve when you turn on the water.