I think the concerns raised are valid but maybe overly cautionary. That said, I can’t see the photographs properly - they’re tiny on my phone screen.
The damp shelter; fix the roof as needed and add gutters if needed to get water away from the footprint (or to a Waterbutt with automatic nipple drinker). put a wire mesh door on it to ensure good air flow and light year round. I’m assuming it doesn’t have a pool of water in the winter or anything.?
A high perch, with a ladder up to the perch and a nest box will be fine.
I see no reason to add a floor of pallets or Lino. Straw or wood chip/sawdust would be good, especially in the winter of they’re going to be inside a lot. Typically add fresh material through the winter as needed then remove in the spring to compost for veg bed.
A grandpa feeder or a barrel pheasant type feeder and check they learn to use it and you don’t need to feed daily.
Your Heras fencing panels and/or wire mesh can make a small run which’ll do for bird flu confinement for 4 hens and will suffice while you clear further sections of your ground of metal and rubbish.
Cut a small “pop hole” door within your “man size” mesh door to make access easier (small doors don’t smash about in the wind and stop some access, like big dogs.)
There are automatic door opener/closers you can buy, but I’ve not used these.
A light on a timer in winter in hut will improve laying.
I’ve seen foot infections in hens but not realistic to think hens feet are as delicate as humans; they run across stubble fields and gravel. I like to see my hens on the lawn but they’re just as happy in dust and rank weeds; they often chose this over the lawn.
Fencing can be creative: looks like there’s some good boundary walls and shelter, so a few posts and then panels of some sort should be able to make a good enough pen. Perhaps you could tension a wire from the hut to a post on the perimeter or into walls? I’ve known people who’ve been fine containing birds with nylon netting about 1.2m high attaches to bamboo canes or similar with no electric. Often thought builders barrier mesh might work. -I’ve also had to rescue hens and wild birds from a tangled fate, so it’s not ideal, but nothing is!
A couple of strands of electric is good for keeping predators well off your fence. Until you get hens or talk to neighbours you won’t know what the issues are. Some people have persistent foxes which endlessly dig and figure out ways in. I’ve also friends who’ve kept garden hens for years and never lost one to fox and mostly leave them out often. I always shut my birds away, lost four this summer, two gone broody in hedges and two taken in the day.
Not many cats will terrorise hens.
For outdoor flooring, wood chip is great, bigger chunks the better. May get it free from a local tree surgeon. The top dries after rain and they like it. It eventually rots down and you can put more on top.
Good luck