just a bit of experience here but I have seen the chrome nut on front of pump were you vent pump there is a shaft behind this nut which indicates that pump is working but in fact it is not what I am saying is this spindle runs but the impeller stays put thus you have no circulating Nock off the two valves both side of pump loosen 4 allen screws run pump see what happens ? Impeller should run if it does not this is your problem
Don't get that bit. Only works if the heat input is known. Maybe gas flow is measured, or a relation between gas valve and flow is assumed, and h/ex efficiency assumed.
It's a safety mechanism, not a control one. If the differential is above 25C and below 30C the boiler automatically runs at minimum output. It the differential is 30C or greater the burner shuts down.
The main control mechanism is the flow temperature. If this rises above the set temperature it means that more heat is being generated than the radiators can emit, so the boiler modulates down until the temperature is correct.