theres no point going to the expense of going to fully pumped on a boiler that old you can wire a programmer and thermostat to this setup clock needs to be set to gravity and theremostat will switch the pump on and off you can not select heating only with this system
sounds like mains cold and gravity hot opening the basin tap drops the mains pressure and then the hot comes through
pressure reducing valve on the shower feed should work
i would be looking at the mixer assuming it worked previously the we must assume it has the correct type of pump the pump works when the basin tap is used so it would appear the pump is functioning which only leaves the mixer not passing enough water to kick the pump in check for filters blocked...
you need to decide what system you want, theres plenty of info on the web.Then get quotes ,BG will recomend the system and boiler they make the most profit on personally i dislike glow worms now plastic tat take a look at the intergas boilers all metal with most of the common failure components...
is there water in the black tank have you bleed the air pip by the cylinder to be honest that lot has served its purpose and needs replacing with some thing more economical i thought landords could no longer rent properties that didnt meet a certain efficency rating that set up will be very...
one trick when you get a pipe thats too high is use a macalpine tubular trap and put a trap extender between the u part and the outlet elbow just forms a deeper trap