>>5152951. A few big bottles of water, it depends what you're using the water for.
2. There MIGHT be chemicals. If you're in a woodland with a little flowing river or stream you're fine, if the river goes right next to agricultural farmland then you can't filter any chemicals.
3. Hit its head with a stick. If you have a rabbit hit it at the back of the head near the neck, a wood pigeon you can hit it's head with a stick and it'll die instantly.
4. It depends. If you're sleeping right next to a fire you won't need any blankets but you'll probably want wool blankets or sleeping bag.
If you want to trap or kill game use a slingshot, bow (illegal, but if you have one it's a great way to shoot game) or easy snares. Snares are great. Poach whatever, it's fine to hunt small game that are pests in the UK without "permission" bullshit. No one even gives a shit. If you don't get caught you'll be fine.