A: You can take the normal underground / tube (same thing) from Heathrow to central London. It is the Piccadilly Line, but it doesn’t go to Paddington directly (you would need to change lines.) It also would probably take around an hour at least to get from Heathrow to central London (e.g. Piccadilly Circus) using it.
Q: Is there an underground train or tube that I can take to Paddington? The Heathrow Express is quite expensive. Do you know how long it would take to get from Heathrow to Paddington by train? And if I get a travelcard…would that cover both busses and tubes/underground train? Actually, I ‘m not sure if the underground train is the same as the tube?
A one day travelcard would cover tube and buses, or you could buy simply a bus travelcard (cheaper).