Now this is a real testor. I think it has to be a farce question. Anybody else living in the premises? Cold and/or hot water doesn't come out?
A loose bolt or screw is the most common cause for a leaky faucet
You have a high iron content in your water. There are systems to correct this but there not cheap.
the water pipes of the 2 items are probably connected in the same pipeline. Poor venting or a stoppage down stream
The faucet is clogged
There is a ball or cartridge in the faucet that diverts the water to the sprayer when you use it. These can become stuck from minerals in the water. You can take it apart and put some CLR or full strength toilet cleaner in it and let it sit for a while. The toilet cleaner can cause burns so be careful with that. Slowly turn the water on just a bit to flush out the cleaner and reassemble. Turn the water on, Hot, hold the sprayer and tap the side of the faucet at the base of the spout with the handle of a table knife or similar weight metal. The vibration may cause the ball to release.
You can look in the phone book for a good plumber. you could also try not putting anything in the toilet that would cause it to clog. Hope this helps and stops your toilet form over flowing and getting all over the floor.
A clogged aerator on the end of the faucet would cause the water flow to decrease in that faucet.
It means that you should sell your home and move far away! No jk If its your faucet that is dripping I think in time your faucet needs repaired or replaced because if it drips only when you run water at another fixture (faucet) and doesn't drip if you have everything off then you have a strange faucet but its most likely caused by water hammer (sudden stop of water flow) and if you don't think its cause by that then it also could be from water pressure which when you turn on another faucet and the pressure drops a little and from the drop of pressure and it vibrates your seal in your faucet which could make it drip but very rare but possible.
Yes, you can adjust the toilet clog to clause your toilet to overflow.
excessive velocity
Nothing, it can not do that .
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.