Hi Lizabeth and welcome to UKY!
First things first...take a deep breath and repeat after me: "This is going to be ok. I can do this!" We're here to help and lots and lots of us have gone through what you're going through right now, so you've come to the right place.
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First of all, I highly recommend mailing your forms and documents in for your fiancee visa. I know lots of other people have done it in person, but for me (being in TN at the time, and my consulate was in NY too), it worked like a dream. As long as you have all the documents they require, you should have your visa in hand and all the original documents you sent to them within a week or two. (You can read about our experience on my website if you want to hear all the details. Keep in mind that we did ours in 2001 before the charges and rules changed slightly.)
As for giving notice for your wedding, we got married in Scotland and did not have to be in residency or anything for any given number of days. My husband lived in London then, called up the Aberdeen registrar and took care of everything like that. THey had to have a copy of my birth certificate ahead of time, but I sent that to them while still in the US. I then arrived in the UK 2 weeks before the wedding, and it was all just fine.
You can check out this site's forum
http://www.weddingguide.co.uk for lots of helpful info on the requirements for weddings all over the UK.
We were living in a flatshare when we first got married, but were quite clearly told that that was not allowed when it came time to apply for our FLR. So we stayed there for about 6 months, and then moved into our own flat. We were questioned about this at our interview for the FLR, too, so unless that rule has changed, you will need to be able to support yourself.
Croydon in person is the only way to do it, as far as I'm concerned. It's a great bonding experience for you, anyway!
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The Home Office does not have a good track record for returning things promptly...unlike the consulates in the US. Just take snacks.
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Hope that helps a bit!!