Check that the black rubber taper ring hasnt got pushed inwards , remove nut and put on pipe , put on thrust washer if supplied then tapered rubber on , thin edge to trap then assemble trap to bath with a smear of silicone on bath threads and tighten up then fit clip outside to hold pipe still
Might contain an old Galvanised water tank I have found this before , a solidly built t & g box using sawdust for insulation often in those built or upgraded early 20 c
The main boiler pump should supply hot water to the manifolds, zone valve and cylinder zone valve. The pumps on the manifolds recirculate the water through the uf pipes via the thermo mixing valve which just keep topping up with hot water unless you have a low temp supply eg heatpump when you can run direct.
There should be an auto bypass after main pump - see boiler manufacturer's brochure for info
Putting a pipe onto the kitchen mixer tap (high pressure cold low pressure hot ) will have caused a back flow up into the hot water cylinder and up into the cold feed tank and then to overflow