That depends on where you are travelling from.
No
No
There are no rides at the London Dungeon.
No
no
Yes
Liverpool Street.
Euston
No.
To enter the United Kingdom, you will need a passport and, from many countries, a visa. Once you are in the United Kingdom, you can go to London freely: there are no internal checkpoints.
You do not need a transit visa, if you do not go out of the airport to see London or change airports at London.
It depends which country you are from, you do not need one for the games themselves but you may need one to enter the country.
London is an expensive city to visit as a tourist so you need to be quite well off to be able to make the most of your stay.
Bedford is approximately 80km north of London. To travel by train you would need to go to St Pancras station in London or by car take the M1 or A1 from London and follow the signs.