The plaming tubes are all conected.When the cold water run in kitchen the cold water at the shower become less,so with less cold water at the mix cold-hot (the balance is desterb),making the water hoter.Same if you turn on the hot in the kitchen the water will be colder in the shower.
If you assume that the water entering your house in the mains pipe is at a constant pressure (this is a relatively good assumption) then the more outlets you give for it to flow from, the lower the flow rate from each one. Say you are supplied 1 litre per second and your shower is using all of this. Now, turn a tap on to 0.3 litres per second and there is 0.7 litres per second coming from the shower head. Showers are often upstairs and kitchens downstairs, so if the tap in question is in the kitchen then the effect will be greater than if they were both on level. The pressure of the water in the kitchen tap is made larger by the head of water pushing down from upstairs, and when both are turned on, the kitchen tap can "steal" more of the shower's water than a bathroom tap would when twisted the same amount.
The kitchen is probably closest to the water heater and the shower is the farthest. Water cools down the farther it travels through the pipes.
There is a main drain that runs from the basement through the roof where it is the vent for the system. If you look at the layout of the house, the upstairs bath is most likely over the downstairs one or the kitchen. If you look on the roof, you will see a 4 inch pipe coming through the roof that should be over the upstairs bath. The sink and shower drain into that and then to the basement and out of the house. Most likely the main stack is in the wall behind the toilet.
Stoppage
Bad shower valve.
Temperature balance shower body needs to be adjusted
The main drain is plugged. Not completely, but enough that it is easier for the upstairs water to come out in the shower and floor drain instead of going out the drain.
Insufficient water pressure or incorrect pipe sizing
You should let a professional do that, incase there is more damage that you can not see that the water has done.
Unless it is a very strange arrangement, turning off the toilet on the first floor should only shut off the water to that toilet. It should have no effect on the upstairs shower.
it sounds like there are crossed lines. if there is no water upstairs there has to be a valve that is off. even if there is low pressure it would eventually fill the line and you would get some water.
Do you have an upstairs tenant or the sewer is backing up.