No
You can't travel directly from Heathrow to Bristol. The best way is probably to take a bus to Reading and get a train from there or travel into Central London and get a train there.
Eurostar train from London to Brussels is 2h 01m, London to Bruges 3h 25m
There is not any direct rail connection between Belfast and France. You will need to travel via London, using ferry service. It will cost you $90 to travel from Belfast to London (ferry and train both), and another $117 to travel to Paris from London via train.
Journey by Train, Because I love train journey.
train
Drive or take the train.
You can't travel directly from Amsterdam to London by ferry because London doesn't have a ferry port. You would have to travel from Amsterdam to Hook of Holland by train (or drive), catch a ferry to Harwich and then take a train (or drive) to London.
2o hours
Two days.
Train from Paddington
Not directly. You will have to travel into London and get a direct train to Carlisle from Euston Station.
No, but when you get to London you can use your bus pass on London buses.