It may be the wastes that the plugs attach to which are leaking. Also look around the perimeter of the sink is it well siliconed and no holes? It can seep through there.
Result is broken pipes, so symptoms are: 1) no Water at faucet 2) leaking water elsewhere.
Plumbers are people who earn a living dealing with pipes.
Are you talking about pipes under a slab here? If so you probably have a hot water line under the slab leaking that is heating the water in the cold line.
It is the water rushing through the pipes creating a pumping sound
The kitchen is probably closest to the water heater and the shower is the farthest. Water cools down the farther it travels through the pipes.
If it runs continually, as you say, then it can only be the inlet water pipe or fitting, leaking.
Clogged drains are caused by the accumulation of sticky material in the water pipes. Many times stuff like hair, food, plastic pouches.. gets stuck in the pipes and starts accumulating. Because of this the water from the kitchen or shower sink takes time to drain. Many times the drain pipes emit foul odor. Once the pipes are blocked, either the water stops draining from the sink or the debris starts coming out of the sink and toilets. The clogged water may also start leaking and also rust the pipes.[Source:A-General Plumbing and Sewer Service]
A water faucet is the mechanical device fitted to the water supply pipes over bathroom and kitchen sinks. When turned on they supply water.
Its not bad as long as they are not leaking. Unfortunately polybutylene pipes have the best chance to start leaking at some point and it can be costly to repair.
I take it that you mean that it's leaking water and not exhaust gasses. If it's the body of the cooler pipe that's leaking, then you'll have to find a good stainless-steel welder to repair it, or get a replacement. But if it's just one of the pipes to it, then replace both pipes whilst you're at it.
The cast of Light Hearts and Leaking Pipes - 1920 includes: Zip Monberg Virginia Warwick
Is the water still leaking? If so was the original line disconnected?