Shellby
1) It is possible to visit ATC sites but I would only recommend it if/after you pass Stage 1 or 2. I visited Scottish @ Prestwick before my Stage 3 and then the Glasgow Airport Tower once I was put on the Aerodrome Course at College. They expect you to visit somewhere for the Stage 3 interviews (although they don't specifically tell you to). The best way to go about it is to contact the HR department and ask if they can arrange a visit to a site near you.
2) The maths is not difficult. If you can multiply/divide by 6, are able to change hours into minutes etc you should be able to do everything asked of you in Stage 1. Even after that, things don't get much more difficult. Just a decent grasp of the main arithmetic functions.
3) Most tend to be Uni grads (myself included - in Aeronautic Engineering as well) but I can assure you there will be people at the tests that just want a complete change of career like yourself. I had one guy at my Stage 3 that was in his final year of Law and he didn't want to do anyhing but be an ATCO....
NATS don't discriminate against people without degrees, if you pass the set tests to the standard they require then you'll get put to Stage 2, regardless if you're an academic or Joe Bloggs the fence painter.
4) They travel costs can be excessive I agree. I spent about £650 over the year to get to each Stage, and then to Gatwick for the medical. Unfortunately I believe NATS view the costs incurred as an indicator of just how serious you take the tests, just as much as how much detail you remember of the information for stage 1 or if you arrange a visit/do your own digging to find out about the company. I think you can apply for some form of reimbursal, double check the emails/website though.
5) Atlantic House is about 2 miles from the front of the terminal at Prestwick. You could walk it in about 20 mins, it's a relatively straight road but i'd recommend taking a taxi. It's Scotland, our weather is rotten and you'd enjoy the tests much better if you arrived dry and relatively relaxed!
I'm starting at the College in 10 days after 2 years of applying. Believe me, it's worth it if you can make it through. Just keep at it and work hard.
Good luck!