The gas heater should be on the lower level as heat rises, so your feet will get cold in the lounge. Opening up that short wall will help a little, as would ceiling fans to blow heat down from ceiling, but it will disappear up the stairs anyway :(.
Concrete tiles prob better option than retrofitting polished concrete. Don’t paint timber stairs if you are going industrial look. Wall at top right of steps is prob there for privacy.
Not sure where you want tv I can on,y see pic on stairs.

Agree with CP, live in a while and feel the space.
However, these are my suggestions:
Staircase- engineered flooring would be fine. What are the stairs made of. Steel,wood, or concrete? This will determine how easy it is to change.
Mezzanine- Glass, in my opinion is a cold product, not a natural finish. I would recommend wooden balustrade across mezzanine and down the stairs. I would first check the safety standards, and enquire whether you can remove the wall, and the correct height of any balustrade to be installed. The wall also does give privacy for upper room.
Living dining kitchen floors- concrete look porcelain tiles would be the best option.
Sliding doors-yes bifolds will be good.
If you remove the blue wall, you are left with a dangerous step. You could install the same balustrade as stairs and mezzanine.
Faux wood beams- sorry no! As said in the word, they are fake. I would recommend installing shiplap on ceilings. You have a wonderful high ceiling and it could be a real feature.
Have fun with your new home. Hope your budget meets your dreams.

Alternative colouring,

@dreamer, this shiplap picture looks so so good! This look is definitely something that I'm chasing.

@CP, thanks for your advice. I think you're right and to live in it for a short while to see what actually needs to be done. I think I'm just excited in anticipation while I wait to move in 😁

@Kate, I'll upload this wall now. Didn't realise it hadn't uploaded. I've just been googling the concrete look tiles and these could be the go instead.

Thanks again for your advice 😊

I'm going to take a wild guess this was built in the 80's , and originally had carpet ( probably the same cream as the stairs ) in the lounge and probably the dining area .

It seems like 2 or 3 people have had goes at doing 'stuff' , and it's now just a mix and clash of designs .

The wall colours are 'old' ; the tiles are okay but colder than carpet ; the wood look whatever on the floor is just weird ; the carpet worked on the stairs so presumably was just left there ; the low wall IMO is a great feature , but that blue is dated . The wood on top is nice and warm .

There are creams , there are beiges , there are yellows ; there are grey vertical blinds ; there are wooden horizontal blinds ; there are black round railings ; there are wooden railings ; there are thinner curved rails on the front door screen ; the fire is brown ; wooden railings a different brown ; sideboard different again ; coffee table a different brown ; the front door is a darker grey , the windows beside it lighter grey .

SO . Paint every wall in one colour . NOT grey . It isn't a grey area haha . Maybe a warm English Cream . MAYBE white walls but only if you promise to add 2 or 3 large really colourful abstract pictures .

The floor -- I'd opt for wood slats . Faux if you want , as long as they don't look plastic and shiny . Leave the stairs in the cream carpet , rip up the floor and foyer and dining tiles , do all the floors in the wood .

Or re-carpet them again . But don't do polished concrete or engineered concrete or faux concrete or concrete effects . And tiles should only be in kitchens , wash-house and bathroom IMO .

Stain everything wood a really rich brown brown . About the same shade as the wooden venetians . Possibly keep the venetians , change the grey blinds to wood , or at least dark brown cloth . I think the door surround is aluminium ? I'd actually be tempted to change it to actual stained brown wood , but possibly 'just' get it re-powdercoated a deeper brown . Paint or powder-coat the 'arch' front screen a rich dark brown too .

Add the large abstract art , the TV wall mounted -- a lot warmer , a lot richer .

Which leaves the front door -- replace with a nice solid wooden natural timber one ? Paint the existing one ? Charcoal paint , or bright red , bright yellow , bright orange , apricot may suit , purple probably not . Save it for last , see what you think as far as colour goes .

Your home is a very modern design leaning towards minimalist in terms of decor.

I would keep carpet on the stairs just not that particular carpet. Being able to deaden the sound of traffic on stairs is really important since your room is quite large with a high ceiling. Good chance you will get an annoying echo or amplification of traffic in that room with hard stairs. A nice hard wearing textured carpet would be great on that staircase.

I would definately make the flooring on the lower level all one type, not sure a polished concrete look will feel homely though. Given the steel railing on the stairs and lack of interior finishes such as mouldings it could end up looking very council chambers or public library-esque. I actually think the room needs warmth and red/yellow toned real hardwood flooring would bring some magic to that space especially against the steel rail and minimalist design.

The half wall feature is needed to create a livable and cosy space in that vast room by creating a feeling of enclosure in the sunken living area. I would keep it and go one step further with a decorative partition on top of it that reaches all the way to the ceiling. Defining the living space while keeping the open plan feel. Like this...

At the moment the worst thing happening in that entry is the 80's paint scheme and lack of architectural features. Putting a nice modern feature in and making the blue and cream walls go away will work wonders.