http://www.millenniumhotels.co.uk/co...ton/index.html
is a pretty useful site. Maps and links to info on the transportation options. I usually just go to a place and then stand and read the options on one of those machines. Seems any of the advanced purchases involve extra fees and such, and the web sites don't always include all the possibilities. There are sometimes advanced-purchase/USpurchase deals but I think it tends to be a wash. I figure the locals are getting around somehow, and that will work for me. (Admittedly, this method can be trickier in other languages - once mistakenly read German "stunde" for student rather than hour and the whole thing then didn't make a lick of sense.) I haven't ever had an Oyster card so can't comment on the specifics of that. Nowadays you can usually even use your credit cards in the machines.
I purely love riding that London underground. A little scruffy, but I figure it is an authentic London experience. And some of the stations and trains and areas are lots nicer than others. With an all-you-can ride card, you can explore freely. Again, it's been years, but I seem to recall the area around where you catch the Chunnel train especially interesting.
A fridge is included according to their web site. I didn't test the wifi or gym situations.
As I recall, there is a regular grocery store up on the street where the entrance to High Street Kensington tube is. Cross Kensington High Street and break left (west) about a block or two (it's been years though, my memory may have slipped, and it may have moved). Do ask somebody there - clerk in the nearby Boots? Also lots of other food options in the area. Department stores seem often to have grocery stores in their basements. Lovely fresh pre-made sandwiches, pastries, fresh fruit, etc.
Cash - I usually just pull a reasonable amount out of the nearest ATM when I get off the plane. Check your cards for the fee situation though. There is a lot of variance from one to another and you might learn one is better than the others.
I did the Eye years ago. An amazing experience and I loved it. Don't remember the lines as being a problem, but that will vary by time, date, etc. I'd guess the locals have already done it, and you will just be competing with tourists.
Sounds like a wonderful trip. Don't overplan. Some of the fun comes from seizing the moment while you are there - concert in a park, street musician, ??
Romelle