I'm afraid it might be a bit frustrating since it's not pure grammar. Sometimes people prefer one over the other, sometimes it's awkward to say one form in place of the other. Also the context can change things, but generally speaking:
'car door' is a type of door which you can see on cars. In 'noun + noun' structures the first noun can express some attribute of the second noun. 'Door of the car' becomes more specific and the realtionship changes from an attributive to a possessive one. You're talking about a car that we already know of and the door belongs to that car.
'Tonight, we're with the film director Luchino Visconti.'
Here for example I wouldn't say 'a director of the film' because I'm generally talking about his career.
'Hint: the director of the film is also attending the NYFF to premiere his new work Holy Motors. Can you guess now?'
I wouldn't say the film director here.
The same is true for the rest except for 'life way'. I wouldn't say that; I'd definitely use 'way of life' because it sounds more natural to me, although it seems to be a word already:
(Notice the spelling: no space between the words)