Sometimes it will back up from a dishwasher (machine)
Replace the faucet.
run it under hot water in the sink
The smell coming from your bathroom sink when you run water may be due to a buildup of bacteria, mold, or debris in the drain or pipes. This can cause unpleasant odors to be released when water flows through the sink. Regular cleaning and maintenance of the sink and pipes can help eliminate the smell.
To install a water filter under the sink, first turn off the water supply. Then, disconnect the water line and install the filter unit. Connect the filter to the water line and turn the water supply back on. Check for leaks and run water through the filter to ensure it is working properly.
It sounds like the water heater is so far from the kitchen sink that a recirculating line may be required to keep the line feeding the sink hot, otherwise, it will cool down causing you to have to run all that cool water out before the hot gets there. The reason you get it faster when you run the bathroom is because you are drawing more GPM through the line with two fixtures on.
When water disappears down a sink, it goes through pipes and either goes into a septic system in the city or a septic tank in the country.
Neither, because you want to lay down on your back and it is impossable to sink in quicksand. But from walking or running your would walk.
Probably not, depends on where the clog is at and how the dishwasher drain is connected. I wouldn't chance it, but the worst that will happen is the sink will fill with the water from the dishwasher.
You probably have a blocked or frozen pipe into the H/W tank.
If indeed it is IN your sink, simply run lots of hot soapy water through it.
The discharge line (soil ) may be slightly back pitched so it takes longer to drain
I assume it is the bathroom sink. Is there hot water in another sink in the house? In old steel pipes I have run across ones that get so rusted on the inside that water can not get through them. If anything has been done to the hot water line anywhere in the house, sediment or rust may have broken loose and plugged the fixtures.