Well I work in the City and you will normally pay £3 for a pint of lager but some places you can expect to pay up to £6.........Especially if you go to clubs and flash bars. Things you should see whilst in London I would say would have to be the Tower of London, Parliament and of course Buck House. The london eye is a good way of getting a great view of the city but it depends on the weather.
It is starting to get a bit colder but nothing to bad as yet. I would imagine it will be around the 10-12 degree mark during the day and possibly down to 0 overnight. Also bring clothing that will keep you dry as no doubt it will rain at some point
if you find a Starbucks in London they sometimes have free wifi. Also in some McDonalds.... Otherwise there are plenty of internet cafes around the place that will charge you for airtime, although I do not know how much...
Hope this helps a bit