Eastbound District Line to Turnham Green – car 3 or 4 I think would be best. Change direction there to Westbound District Line (towards Ealing Broadway) to Acton Town (any car). Change there (cross platform interchange) for Piccadilly Line towards the Heathrow stations (note, Heathrow Central is the name given to the Heathrow Express station served by main line trains from Paddington. It is nearest the underground station serving terminals 1,2, and 3). Not too sure about the alighting point at the Heathrow stations as I have never travelled to Heathrow by tube.
Mornington Crescent, Jake? Causes confusion (and was obviously why the sub-game in “I’m Sorry I haven’t a clue” was named thus). On the Northern Line between Euston and Camden Town. Both branches (City and West End) of the Northern line run between those two stations but only the West End branch serves Mornington Crescent. This is chiefly because, whilst the West End branch is aligned roughly north-south at Euston, the City branch tunnels are actually heading slightly south of due west when they leave Euston towards Camden Town. They turn in a fairly sharp arc on leaving Euston to head north but do not actually go near Mornington Crescent. Although the tube map shows the City Branch as being east of the West End Branch at that point it is in fact west of the West End Branch tunnels that serve Mornington Crescent. (The City branch passes under nearby Mornington Terrace and Arlington Road).
All done without Googling anything so I’m off for a lie down.