Hi Smnbyt,
The leak symptoms you describe suggest to me the water pumps pressure switch may have become faulty and is allowing the cold water pressure to rise above the normal 0.7 to 1.0Bar. If the pressure switch fails to operate correctly, this type of pump is capable of producing dangerously high pressures, and this can lead to pipes and fittings and appliances being stressed and causing leaks. Check your pumps hand book as it may give instructions on how to reset your pressure switch.
Your water heater delivers hot water by displacement. You have to pump cold water in to get hot water out. The heater is designed to keep a small air cap in the tank to allow for the expansion of the water when it is heated. This can cause a rise in hot water pressure over the cold supply, and when you turn on a hot tap you will often get a surge water before the pump kicks in. When you turn the hot tap off, the pump will run for a little longer to re-establish the pressure in the tank, but this should not be more than about 5 to 10 seconds tops.