Your post is confused. You can use home bank only for first application out of country. You can use income instead or in conjunction with savings with a proof of income from your home embassy if not applying in your home country
You can apply for a fiancee visa which permits your partner to travel to the UK for the purposes of marriage. If she comes on a visitor (tourist) visa, you won't be able to get married as most places are required by law to check as to visa validity
I used my Thai DL as proof of residence to get ETD from British Embassy even though I was only on a tourist visa, and went to Cambodia before returning to Thailand to get new passport. I needed to transfer the remaining validity of my Thai visa into my ETD before leaving Thailand. I had no problems leaving or re-entering and my new passport was back within 3 weeks
When I did my extension last year, I turned up at 6am, and finished mid-afternoon. The people turning up after 8am when they started handing out tickets (I think about 18) were being told to come back the next day, as they were no longer issuing tickets for that day, so maybe you've been lucky so far