Relative to other leading European and Western cities, London is a bit smelly, dirty, stressful, and unless the sun is shining, it is grey and miserable. But everyone gets used to this and the positives of the city often outweigh the negatives, but as soon as you leave for a long period of time and then return, the negatives smack you in the face and once again you have to habituate yourself with your surroundings. Doing a PhD in London is a great way to experience the city on the cheap, but on £15k a year you'll have to strictly budget. I wouldn't necessarily recommend pursuing an academic career in London though (simply the pay is too poor unless you want to continue living a student-type life).
1. Do all PhD students also have to pay a fee every year?
As said below, it depends if you're an international student (if so you'll have fat fees to pay). If you have UK/EU status, your fees will be covered in standard funding.
2. What exactly are residence halls? What do you share with others? I'm not exactly a social type. Is it easy to have your own accommodation that you don't have to share?
Halls are just student accommodation. In London, the quality varies immensely. When I did my Masters I remember visiting some utter dumps, and that put me off student accommodation for good, since then I've opted to rent a private flat. However, all the leading colleges have built nicer student accommodation to attract international students - last time I looked it cost between £78-£120 per week. You will probably have to share a self-catering flat with 4-6 people. Look at UCL's own accommodation or UoL's accommodation pages. UNITE also provide private student accommodation.
3. I read most people try to avoid traveling because of the costs. The PhD I'll be doing will involve going there every work-day. What accommodation is the best?
A number of UoL halls are located next to UCL or very near.
Get an Oyster card and a Young Person's Railcard Card (if you plan to travel outside London).
4. How much does health insurance cost?
You can buy private health insurance, and/or I think most students on long courses get free treatment on the NHS. Most EU countries have reciprocal arrangements.
5. Do PhD students try to save for a pension?
Generally no, you won't have enough money to do so.
6. What are the general work rules of a PhD? Can you easily be fired? Are you entitled to holidays? etc
Holidays are normally 6-8 weeks - this will be outlined in your regulations. You can't be 'fired' by your university, because you are not employed, and therefore, also have no protection under employment law rules. It is possible to have your registration terminated, but this never really happens.