TIME for a replacement
If water is only drawn from the cold faucet, then no, the water heater is not involved. However, if water is drawn from the hot faucet- even for a few seconds- hot water IS withdrawn from the heater, and fresh cold water drawn in to be heated- even if the hot water did not make it all the way through the pipe to the faucet- and the water heater will work to heat that fresh cold water.
It is very likely that it is sediment in the screens of each faucet. Take the screen off the spouts and see if that's the problem.
Yes
If you have an instantaneous hot water heater, and your faucet doesn't flow enough water it won't turn on the water heater. Thus requiring another faucet to be turned on.
Generally this is caused by pressure being built up from the water getting hot in the hot water heater. By code you should have a hot water heater expansion tank on the cold water inlet of the water heater to absorb the added pressure. If this is your problem, the excessive pressure could possibly burst your water heater. The faucet stem or cartridge or washer may be loose or moving and blocking flow.
Water is coming down from upstairs or it is back pressure from the water heater. If it is the water heater, it can come out of either side of the faucet.
When you want to know when your hot water heater is broken, simply run your faucet and test the water. If it's cold, the heater is broken.
The water is not circulating through the heater core or you have a control problem. If the heater is putting out heat then it is probably a control problem. If no heat then - water pump out, low on coolant, or maybe the therostat is stuck open.
Check the temp on your hot water heater, you can turn it up.
Air flows through the heater core to warm it up. Assuming the heater core is circulating water from the radiator, the problem is usually with the blend doors. These doors regulate air flow through the heater core and when they break, they usually block the input into the heater core and kill the heat. Check heatertreater.net for diagnostic information and an inexpensive fix.
Yes, but you will have no heat. Your heater core is leaking and needs replacing.
There are a few things you can do. First wrap the hot water lines from the water heater to the faucets. You can also install a hot water circulation system that basically circulates hot water to the faucet 24/7. This allows you to have almost instant hot water each time you turn it on. You can also install a small on demand water heater near that faucet. It will produce hat water when the faucet is turn on. There is no storage tank on this type unit. They are very small and can fit under a sink.