Well for PhD students most of the work I do is teaching or marking and I also help out on interview days, but most students have that opportunity. Most of my day to day at the moment work is reading papers, writing my literature review and planning my experiments. Although this week I'm also going to be helping to plan a conference happening next month. I've not travelled for my work yet but I am probably going to Germany for a week in the summer for a course. There's a possibility of travelling later in the project but it will depend on whether I need to for my project. On the other hand, the guy on the desk next to mine in my office has already been to Chile, Italy and Germany and is planning on returning to Chile and Italy in the next year or so.
A train from Lancaster to London and back is typically about £90 but is £60 with a rail card. It can be much less (Less than £40) if you book in advance. There are trains running from London to Heathrow, yes. Although Manchester Airport is much nearer to Lancaster and it is an international airport.
Oh I see! I have vaguely heard of Keynes but that's about it. There's nothing wrong with having interests beyond the subject you want to study!
The UCAS website is here:
https://www.ucas.com/And the idea is that you make an account with them and search for the course you want to study. Then you pick five, fill in what qualifications you already have plus predicted grades, write a personal statement about yourself and submit one reference/letter of recommendation from a teacher or someone at your school. There is also an administration fee but I think it was £20 when I applied, so nothing too major. When you've sent your application off the universities will review it and they'll usually do one of a few things:
a) Give you an unconditional offer. This is quite unusual but basically means that you have the requirements for the course already and they're happy to take you on.
b) Give you a conditional offer. This might be something like "If you get three A grades then you can study here". This is probably the most common result that people get, well this and the next one...
c) Ask you to come for an interview. As you're international they'd probably let you do this over skype rather than expect you to fly over just for one day. After the interview they may do any of the three other options.
d) Reject your application. This does happen to some people, but usually when they apply to a university that is much beyond their abilities.
Then depending on when you get responses from the universities you have to make a decision about where you want to go. So you select your first and second choice from whatever offers you have. Then you pretty much wait until you get your results and then you place is confirmed if you have a conditional offer
The time scale is usually that you need to apply between September and the middle of January for entry in the following September/October. So if you applied this October you would be looking at 2017 entry. If you want to come sooner then it would be worth contacting the universities you want to apply to directly to see what they can do, but they will probably tell you to apply for 2017 entry. Does that help clear things up? The UCAS website has a load of information on how to apply and so on.
Do you know roughly when you'll be visiting, by the way? Just so I know whether or not you're planning on being here during a holiday or anything important for me.