Unless there is a recirculating pump the hot water has to come from the hot water heater. Depending on how far away it is from the faucet, it can take 15 to 30 seconds for the hot water to get there. Since there is nothing in the pipe to keep the water hot, it cools down between uses.
It's probably not the faucet. It could be that there's an obstruction in the hot water side of the fixture, but it's more likely that the hot water isn't getting to the fixture in the first place. The easiest thing to check is that the hot water valve at the wall under the sink is on.
The seals in the faucet most likely need replacing.
A faucet.
mostly because of rust deposits
If it had been working fine -- then if it is a cartriage type -- replace it --
First make sure that the hot and cold supply lines (the plumbing) aren't backwards (hot should be on the left as you are facing the faucet) or that someone accidentally ran two hot lines. For the problem to be in the faucet itself you would have to have a single handle faucet. If this is the case the control valve is broken and should be replaced. Three handle Left= Hot Water Flow. Right= Cold Water Flow Center= Controls whether the water comes out the shower head or tub faucet. Two handle Left= Hot Water Flow Right= Cold Water Flow (Diverter Valve is elsewhere if it's a tub/shower) Single handle One handle controls both water pressure and temperature
Tap water comes from the water faucet. It gets to the water faucet from the water treatment plant through the water storage takes and lines.
You probably have a blocked or frozen pipe into the H/W tank.
Faucet needs repaired.
I wouldn't think PVC would attract the calcium particles, at least not to the extent you're talking about. On the other hand, the metal pipes in your faucet will. Try cleaning the faucet first. If you find you have calcium buildup in your faucet, you can either try cleaning it with a product called CLR (Calcium, Lime, Rust) or simply replace it. Good luck.
If the sprayer hose screws onto the faucet, you can get a cap for that fitting. If it pushes into the faucet, I do not believe there is any plug available for that type. You have to have something on the hose fitting or water will come out when you turn the faucet on.
There is a shutoff valve on the cold pipe going into the H/W tank, if you close it no water will come out of the tank. There should also be a shutoff valve on the wall below each faucet/tap.