Wet flooring and architrave, skirting board

I’m assuming the question is why is there wet? This is not something anyone would be able to comment on without with certainty without seeing the property. I’d suggest you look for a leak inside the property - do you have appliances such as a washing machine/tumble dryer or shower/bath nearby - even in an attached room (the water could pass through/under dividing walls (I’ve got a job to do soon where the leak came from a eighbouring flats’ toilet. Another thing to check is the outside of the property in the area where the wet is worst - often the guttering leaking causes damp/wet issues inside a property. Look for wet, or green patches, on the outside. Another possibility, but one you’d probably already be aware of is whether a pipe may have burst inside the property/room affected. The last thing I’d consider is how ‘sealed’ the room is. Do you have windows shut, are air bricks blocked, could there be a big build up of condensation in the room as it will go straight for the easy ‘sponge’ - the wood.

Very hard to say without inspection. If its an old property the ash felt could be on top of a concrete floor and starting to breakdown due to rising dampness

It all needs to come up around wet areas. Could be sectioned out to only remove affected areas to mininalise cost but this must be done or it will cost you more in the future.. But essentially you need to locate & repair the source of the water problem

Sometime with that type of underlay the floor can sweat causing damp not that anyone would predict that with the heat inside and temps differing can sweat