I also would like to encourage other pro puzzlers to join in, although I know that this kind of puzzle doesn't fascinate everyone. Tom_I and Ehhxekt, where are you?
Well, I'm lurking in the background. I haven't visited much recently, but spotted this puzzle yesterday, though I 'm not making much progress yet, other than with things that have already been solved.
But to try and make a start, being of a certain age, I recognise Extra i as overweight private detective Frank Cannon (played by William Conrad), and his Lincoln Continental, from the American TV series "Cannon", first shown in the 1970s. I think the architecture link is with 5, the rotunda in the Cannon House office building in Washington DC (though there seems to be a mistake somewhere, as the "answers" post has 5 as the Domus Aurea, which I think is a different picture).
But the car link is the problem. I thought I had found a Hotchkiss, which would have fitted, but it has already been identified as an Amilcar. So all I have at the moment is the possibility that Car M could be the bodyshell of a Mike Cannon trials car, but it's a bit of a guess.