I'm sorry that you're struggling. It's always difficult to move to a new location.
I 4th (?) Watching the English. It's quite funny. I also found Bill Bryson quite relevant, though I can't remember the particular books. Notes from a Small Island perhaps?
You sound like quite an intense person. I think I was when I first moved here, both down to natality and age. These things that you're asking for are actually quite a lot from a relative stranger. Most people just want a casual chat over tea or beers, not to interface with people. I don't know what that even is, but it sounds all consuming. And on that point, I'm a particularly high strung individual, something that British friends tell me is very American. Brits do seem a lot more chilled out and relaxed to me than my American friends and family.
For emotional immaturity, I think you're getting a bit of the stiff upper lip. It eases with time and deeper friendships in my experience. Same with external processing. Though the pub after work is really great for pushing that along! If you're invited, go! Or ask if others want to join you for a quick one (they say that, it means exactly the opposite in my experience).
Crappy cultural guides. I honestly, hand on heart, found comedy and news programs helped me the most. My sister now watches the latest of Have I Got News for You and things like The Mash Report, every time she visits to re-catch up. It's amusing, mocking, self deprecating, and somehow explains a lot about culture. Though I lean left politically so your mileage may vary.
Hospitality. Nope. Never going to happen. Sorry. And it's annoying, isn't it? I'm obnoxious about introductions I flat out run up to people, play on being American because it allows me to be cheerful and forward, and joke about the British talking for hours but never exchanging names. I own that it's obnoxious, but that I really like to be introduced around and know who I'm speaking with.
Britain is not religious as a whole. It's one of my favourite things about living here. I come from the South of the States. I do not know anyone who is religious and most of friends and acquaintances are openly anti-religious, as am I. Any mention of church, god, etc and I'm out of there. While I may not be the norm, I'm not alone, and I think that being openly religious in a non-religious environment may prove a difficult hurdle to get over when speaking with people you've only recently met.