Yes, even Don in the end I think understood that his fear of being found out wasn't about him really being Dick Whitman, it was his thinking that he was a terrible person, as he believed.
Right--but I think Pete's type of "good family" would see them as weirdo aristocrats. And they'd probably see the New York Dykmans as provincial and uncultured. It's a completely different ideal of what good breeding looks like (even if underneath they might be alike in many unflattering ways).
I also remember having the vague impression that somebody had some connection to nobility--although of course that doesn't mean they're not also a conman or something of a bum. Plus there was the guy who was, iirc, a doctor. They clearly live in a wealthy world. They probably have truly cultured educations, speak many languages, are familiar with lots of places, know about art etc.
Exactly--this totally nails the general impression I had of them. There's something false and empty at the center of them, but it's not connected to the class they're claiming to be from. They're not like Don--but it's no surprise that they would see Don as potentially one of them despite his having come from nothing and would never feel much familiarity with Pete who did grow up in a world of money and there might be a few places they might cross paths.
Of course, Don's also so attractive and mysterious people want to see him as part of their type, but that's not all this is.