Hi Woodlands,
As others have said, the removal of the filter element will not increase the ultimate pressure in the system, but it improve the flow. Water pressure its self should not damage the pressure switch, as teh switch limits the pressure by switching off the pump.
The continued pulsing of the pump whan all the taps are shut, definately points to a leak - somewhere. As others have said it only needs a small drip, just enough to drop the pressure enough to cause the pump to run.
I note you have added a non-return valve, but you didn't specify where, it should be in the single water feed from the pump.
Other places to look for leaks; The 1998 Avondale will almost certainly be fitted with a Carver Cascade 2. Many of the plastic water connections, bungs and valves can deteriorte with age and use, its worth checking them carefully. But hidden from general view is the fussible plug which is buried in the middle of the heat exchanger fin pack (accessed by removing the flue couwl and inner fire way plate.
The Fussible is made with a low meltpoint alloy (Woods metal) and designed to blow if the heater gets too hot. However with age the woods metal can become loose and allow a small leak path. Such leaks are small and the leaked water will either evapourate (if the heater is on) or simply drip out of the bottom of the external flue vent and may not be noticed.
Spares for the Carver are becomming more difficult to find but Gary at
http://arcsystems.biz/ may be able to help