Unscrew the aerator from the end of the faucet where the water comes out and clean the screen. Sediment build up slows the flow.
Mixer valve
It does not affect the temperature directly. What you are experiencing is the reduction in the water pressure of either the hot or cold water by way of it being re-directed to the other faucet. So what you get is less pressure , let's sy of cold water and the same of hot making your temperature hotter. or vice versa you get less hot water and the same cold making yours colder. I'm no plumber certainly but I understand that a larger diameter pipe reduces or eliminates this phenomenon.
Try removing and cleaning out the aerator on the sink faucet, and the shower head. (Word to the wise: if you take them apart, write down the order. It can be tricky trying to figure it out, afterwards). By just removing them, you should get hot water, thereby verifying that these are the cause of the problem. If you don't want to clean them, you can always replace them. Water saving aerators are available for faucets. Water saving shower heads are also available. Some shower heads even have on and off switches, for additional water savings. How I learned, the hard way: My situation was, hot water from kitchen & bathroom sink faucets, and even from the tub faucet, but not from the shower head. So, I removed the shower head and soaked overnight in CLR.* Cautionary note: Probably would have been OK to soak overnight in vinegar, or for a few hours in CLR. But overnight was too long in CLR. It must have dissolved more than just the calcium deposits. Now the shower head has much thicker and much more water consuming streams. (Previously it had a very stingy water conserving spray).
Think of it as water flowing down a hill, but instead of on the ground it is in a pipe. For a typical "Petticoat Junction" type rain-water reservoir that will supply the home with running water, it is the difference in height between the faucet and tank that provides the water pressure to push the water through the pipes. The higher the tank, the greater the pressure at the faucet-- which means higher flow. If the tank was not higher than the house, nothing would come out of the faucet. A city water supply supposed to be around 60psi but can vary greatly depending on the terrain. Since most water is gravity fed from elevated tanks, a home at the bottom of a hill will have higher water pressure than one at the top of a hill. Cities with big ranges in elevation have pumps to boost pressure at higher areas and regulators to reduce pressure in lower ones. The elevated tanks are closed at the top and do not collect rain water. Water is pumped up to the tank overnight while people are using the least amount. During the day, the full tank supplies all the water the city needs. High-rise buildings are fed with the same water supply as the rest of the city, but have booster pumps every so many floors to maintain a reasonably constant pressure over the full height of the building.
P1V1=P2V2 P1V1/T1=P2V2/T2 PV=nRT P=pressure V=volume n=number of moles R=the gas constant 8.31J/molK or 0.0821Latm/molK T=temperature in kelvin
check for leaks
Possibly a pressure reducing valve installed after piping for first faucet, which would cause situation describing.
You have to undo the aerator at the end of the faucet and clean the screen or plastic water saver out. It will be plugged with sand or sediment.
Most of the newer kitchen faucets have "flow restrictors" to limit water use.
You have an old seal. Like a rubber ring in your faucet. Replace it.
Some faucets use the water pressure to open the seal after it has been released by the handle. It may be that the seal is tight and slow to move after it has been released. One other thing to check, is your water pressure ok at this faucet.
The water valve under the sink is turned off or has gone bad. It is possible that there is a blockage in the faucet itself. I'd start by ensuring that the water valve is turned off, and take the faucet apart and look for anything out of the ordinary.
Have you got two single faucets or a single lever faucet? It could be a pressure imbalance or it could just need maintenance
Turning on one faucet will cause a pressure drop at any other faucet that is running, but you say it is a "significant" drop - that implies that you have low water pressure, period. You might to consult with a plumber to see if anything can be done - if you live in a house with very old steel plumbing pipes, replacing them can make a noteworthy difference (it's not cheap, of course). Or possibly, you have an unusually low pressure system, perhaps a gravity feed system. Installing a water pump will solve any inconvenience, such as the shower almost quitting when a toilet is flushed elsewhere.
Low water pressure or cold water main undersized.
Just the same as in a house. - detach a faucet or many faucets, at one end of building and blow in air from the other end.
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.