If the pipes are old, it's most likely that corrosion has built up inside them. Some of this buildup may have become dislodged and clogged the path to the low-pressure faucet.
check for leaks
Unscrew the aerator from the end of the faucet where the water comes out and clean the screen. Sediment build up slows the flow.
Possibly a pressure reducing valve installed after piping for first faucet, which would cause situation describing.
The faucet is clogged
When your faucets are off, the water is sitting still. As soon as you open a faucet, water starts flowing out due to the pressure created by your water pump. Whenever you turn the water faucet off, the water supply is cut at the spigot and now all that water that was moving has now stopped, suddenly. Sometimes, when the pressure is too high, it can cause what is called water hammer. Water hammer is when a faucet is turned off, a shockwave is sent through the pipes, vibrating them sometimes throughout the entire house.
A clogged aerator on the end of the faucet would cause the water flow to decrease in that faucet.
A leak in the supply pipe.
The black build up is mold. Yeah, gross huh? You should try Lysol spray on your faucets.
Lots of stuf can cause it including sediment or a blocked supply line
A whistling noise coming from the shower faucet or when filling the bathtub could mean that there is excess air in the water line. This can be fixed by turning off the major water supply valve and then opening all of the faucets in the home for about 5 minutes. Shut all of the faucets off, then turn the water supply back on.
A loose bolt or screw is the most common cause for a leaky faucet
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.