
As with everything in life you'll get lots of different answers, lots of different paths to the same destination. I do leave puppies alone, right from the very first day but I don't use cages. So I just walk out the room, or go upstairs, no treats given, no fuss made, it's perfectly normal, I'll be back in a minute. No fuss made when I get back, but no need to avoid eye contact either. My dogs are super chilled about being left anywhere, they don't even lift their heads to see where I'm going.
For the car I agree that just sitting in it, playing with her, feeding her, just sitting reading a book on the back seat with her sitting beside you eating a kong, whatever, just be relaxed and happy in the car, when she's super calm and happy to be put in the car then move to switching the engine on, reward calm behaviour, ignore (preferably) or distract anything else. The 1st car journeys are stressful for pups, leaving their dam and littermates, going to the vet etc so you need to make new happy associations with the car. I then progress to driving to my nearest park (literally 200 yards away)

letting pup out to play for a few mins and driving home.
Sounds like you're doing a great job with your first puppy, I wish all new owners were as thoughtful as you.