Hi David,
You did not tell me if its both hot and cold or just one of the supplies that is affected.
Lets clear one aspect straight away. The sporadic pump operation in the night. I assume you have a hot water system. when you fill the heater it is cold, so when it heats up the water tries to expand (which it can because there will always be a small air cap in the top of the heater tank just for this purpose).
If you run some hot water off, then turn the heater of in the evening, then as the tank cools the pressure will drop, ad it can be enough to cause the pump to run to re-pressurise the whole system. Normally this will only happen once my be twice each night until the tanked water stops contracting. The solution is to turn off the pump as well.
If the pump does this several times over night, then that is indicative of a leak somewhere. You may have leak that you cant see. the pressure switch will have a non return valve fitted. This is to lock the down stream pressure in the system. If this is not sealing properly, then the high pressure water will leak back past the valve and back to your main water container.
Some water inlet fittings contain a non return valve. If this is not fully opening, it could give rise to your symptoms.
As previously stated it is difficult to give a fast and accurate solution to problems like this over the forum,. Sometimes it needs an experienced person to go over the system and they might find the problem in a matter of moments, compared to day to-ing and fro-ing on the pages of a forum.