LVT would get my vote. Easy to clean and you can use a steam mop on it too.

We are coming to the end of a house renovation and we had wet UFH installed in all our rooms. It is a bungalow however, it is very unusual property with rooms below the bungalow so it is like a house in some respects. We have a mixture of solid floors and suspended timber floors and couldnt have a screeded system because of the weight. We had an ESP overlay board system installed and have found it to be very effective. Ours is run off an ASHP so I cannot tell you how it would work off gas central heating. Our UFH is on 24/7 controlled by thermostats in each room/area. We did install internal wall insulation on all of the external walls and window reveals and voids beneath the floorboards where possible and my understanding is that this is key to efficient and cost effective UFH.

If you made outer wall then its okay to build window on the side, your neighbor privacy will be maintained and you can get the sunlight needed, I would advise to move the garage to the front so it can be accessible for a car from the main road, you can still have direct path to the garden from the front if you move the enterance to the right and just put a fence, if it were me here's the layout i will do, it'll give more space for closet, bigger bath, utility room, and additional storage unit, so basically move the wall to the left and focus buildng that side, the previous garage will become the new master bedroom with en-suite

Rinked, I also considered that, but the table and chairs would block access to the back garden. The front extension would significantly block most of the south-facing light in the living area, the back double doors, are north-facing so they don't bring in any light. So while I agree that you need some sort of entrance into the home, The front extension is a mistake in my opinion. In regards to the comment of keeping the passage, yes it's good to have, however, soo many people who live in terrace houses don't have that option and I don't see that as a significant issue.