Monobloc tap problem.

That is why one-way valves are "required", though the water board is more interested in being sure your hot water can't make it the other way.

You lose a lot fo flow rate with the non-return vales though, so you might prefer to find a coaxial mixer so the hot and cold stay separate right to the spout.

Yes. Have you checked that the tap is intended for use on low pressure hot water? Damixa is (was?) a Danish manufacturer, so it would not be surprising if the tap is intended for mains pressure cold and hot water.

You may also find as a result that the HW flow, once connected is very slow.

Potentially yes. The high pressure taps often do the mixing in the body of the tap whereas the LP ones tend to have concentric tubes and mixing is at the outlet. This is also for the benefit of water regulations where there is concern that hot water (potentially contaminated) can find its way into the main.

I would begin by checking into the tap type and going from there.

when you read the Damixa destructions they do recommend they are only for mains pressure hot,

I didn't risk it, I returned the Damixa for a Franke Olympus, gives good hot flow, obviously mains presure cold can dominate the hot if you let it, but controls are good.