This is a question i get asked a lot, Repair verses Replace?. My policy is to replace the shower as repairs to old units (eg. replacing heating element at a cost of 180-200 euros) only to have another part fail a few weeks or months later is not cost savvy for the customer and results in callbacks for me and loss of future custom. A new Triton T90xr or Mira Elite ST will cost 420-480 euros maximum (New Unit and Labour).
Modern cisterns are designed to use less water ,you may be able to raise the level inside slightly, but this is only using the maximum storage capacity and may make little impact. Older cisterns were larger and this gave a better flush.
This pipe you describe is from the safety valve on your heating system, plumbers must fit these to protect your system from excessive pressure, however it should not be leaking. Either the water pressure feeding your heating system is to high, or it was in the past and the valve has not closed properly. Get it seen to by a plumber.
This is known as water hammer and occurs as the ballcock shuts down and vibrates slightly , the pipework connected to it amplifies the sound due to it being unsecured and it 'bangs' against surfaces along its route such as timber, concrete , other pipes etc.
There is only one explanation and thats a leak somewhere on the system, since you have not mentioned any leaks its got to be underground somewhere and thats why its not showing up. You need to get this leak located and repaired, as the introduction of fresh water on a regular basis will rust your radiators from the inside out.
Its very expensive even if they came out on the same day that you made contact,unless you have a high-spec apartment the pump would cost 650 euro at most , so you paid 600 euro in labour and vat ,I charge 750-850 euro, so they have 400 euro extra on top for their 'overheads'.
This pipe is the overflow from your attic tank. The ballcock in your attic tank is not shutting off properly, it needs replacing by a plumber, the reason it shows up in the morning is that no water is being used through the night ,so the slow drip eventually fills the tank up to the point of overflowing.
The ballcock is not opening fully (diaphragm washer is worn) or there is debris inside ,restricting flow,in a lot of cases its the restrictor , a small plastic part in the ballcock that should be changed on fitting by the plumber , however most leave the smaller size in ,which is for higher pressure, resulting in a slow to fill cistern. More Plumbing FAQ>>