Not directly. You will have to travel into London and get a direct train to Carlisle from Euston Station.
Train to Kings Cross and then tube to Heathrow.
No
No. You can get a tube train from Heathrow into central London and then an overhead train from London to Luton.
Which train will go to Wolverhampton from terminal 4 of London Heathrow Airport
Underground (tube) train.
Tube (underground train).
Take the East Coast main line train to King's Cross, then get the Piccadilly Line train to Heathrow Airport.
There is no direct train service between Heathrow and Folkestone. You will have to change trains (and stations) in London.
From Heathrow to London - about 15 minutes by train from London to Cambridge - about 45 minutes by train
There are no trains running between Heathrow and Brighton.
There is no direct train between Heathrow and Southampton. You will either have to take the tube (underground) to Waterloo and get a train from there or take a bus to Reading and get a train to Southampton from there.
Not directly, you have to go to the train station in London Paddington and take a connection train from there.