You can drive or take a direct bus service from Heathrow to Oxford.
you can take heathrow express from airport to paddington station , then from there you can take a bus to London St pancras station and then train to dover, or you can use a taxi which can be cheaper if you travel with your family.
This depends on whether you are travelling by car, bus, bike or foot etc.
There are no trains between Luton and Heathrow but there is a shuttle bus service.
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.
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.
There is a very frequent Virgin train from Manchester to London Euston that always stops at Stockport StationStockport is only a few miles from Manchester Airport which has frequent flights to London Heathrow -There is a ntional bus service from Heathrow Airport to the Stockport Bus StationAnd obviously there are hire carfacilities at Heathrow.Hope this helps.
There is no easy way of getting from Heathrow to Croydon. A cab would cost about £50
I am guessing that it will be approximately 15mins-1h35mins. (roughly)
By bus.
The quickest way to Paddington from Terminal 4 at Heathrow Airport is by train. There are 2 train services to choose from. The Heathrow Express is faster (at around 15 minutes) and more frequent, but more expensive. Heathrow Connect takes 25 minutes, but is cheaper.
It depends on where you are at the moment, but once you are at Heathrow, you should be able to locate it, by the numerous signs along the road. If you wish to locate Heathrow Airport, you can find a local map at any bus terminal, travel agency, or just use google maps.