Good evening,
The difference with pump A is that A at the same flow rate would only take part of the water in the boiler (via 3-way valve), the other part coming from return recycling. When pump C pushes it pushes at 14 l / min, whether there is this valve or not.
And yes, adding a circulator completely unbalances the flow rates upstream and downstream of the mixing valve.
Circulator C makes the sampling flow in the buffer tank too large for the overall thermal balance of the installation.
Circulator A runs permanently.
The 3-way flow valve is not motorized. I adjust it manually according to the T outside
The manual adjustment of the mixing valve OK, I do the same.
On the other hand, the circulator of the radiator circuit should normally stop when the heating need is zero.
Hence my room thermostat in circulator cutout, shown in my diagram. If the drawing is continuous, whether in the boiler or the tank, the calories unnecessarily overheat the ambient air.
It is basic, but with an oil boiler (which keeps its T ° constant) and a buffer tank, it is this mode of regulation which it is necessary to choose.
Now it's up to you whether you want a gas plant or save money on heating.
A+
Gérald