I wouldn't advise doing two Master's degrees. I can see why one might be a nice idea (a friend got six exemptions in year at Cass, or Imperial does a two-year one which covers most of the exams - it's part-time though so I think most people who do it are working at the same time), but you can't qualify in less than three years anyway as you need three years of experience in the industry.
You can pass all the exams in that time while working if you're really dedicated - my manager started at 28 with no exemptions, passed them all in 2 or 2.5 years just by working really hard (it helps that he's really smart, of course), and six years after joining on the graduate scheme he is now an associate member (like a partner, but he owns a stake in the company as well). I think one of the great things about the actuarial profession is how self-directed your career development seems to be - at least in my experience (at a medium-sized consultancy).
A lot of people in the profession have maths or finance-related degrees - like you! Showing that you've kept on top of what's going on in business and finance will help you, and also making it clear you've put the thought into your decision to make the move and that you've done your research.
In direct response to your questions:
1.) You would have to start at the bottom, but your experience in the working world would certainly help you with your working relationships and softer skills, and you could potentially rise quickly.
2.) I'd say City, myself, but I reckon the difference is pretty negligible. Not something to worry about in itself.
3.) I wouldn't say two years - maybe one, perhaps while applying for positions in the autumn (although you should bear in mind the risk that shamika mentioned). Either way, I'm sure you'd be able to impress upon employers your keenness to qualify quickly and contribute to the company.
4.) I don't think so! Someone else I know started off working in the post room of his company, then managed to become a trainee actuary, and he's a bit older than most of the other students. Admittedly it would probably be harder to go that route now, but with your degree background I don't see why you couldn't.
5.) I think smaller companies and consultancies would prooobably be more flexible with regards to entry requirements, but I recommend you contact HR departments.
EDIT: I feel I should mention, shamika is a manager, and I am a lowly trainee. About me: I've been working in a pensions consultancy for a year and a half now. I was 24 when I started and had no relevant experience and an extremely irrelevant degree. I took CT1 as a non-member which probably showed that I had the interest/commitment and helped me to get to AC. Of course, that was when I had to admit that I'd failed CT1 - but thankfully my other qualities shone through (or something like that) and they gave me a job anyway ...
P.S. Some dude at PwC once told me I'd "struggle" to get anywhere in looking for an actuarial position. Don't let one recruiter put a downer on your plans - they're not all after the same thing!