Regarding the second point with the cars, My puppy was born on a dairy farm with no passing traffic and came here to a town (mind you, the fact of where she was raised probably didn't make a difference as she'd never been outside before anyway until the day we picked her up) and she was scared of cars too. I never even took her out in my arms before she was vaccinated because there were warnings of parvovirus being around everywhere - newspaper warnings, posters in the vets etc., and they made me paranoid by saying how it is airborne, and that you can pick it up on your shoes when you go out and you should change your shoes and trousers every time you come in from outside before going near your dog

I didn't go that far, by the way!
Anyway, when we did finally take her out, she used to cower and panic every time a car went passed and it was really frustrating....for a week or two until it stopped and I couldn't even tell; you when she stopped being scared, she just did. She then remained scared of big lorries and building sites for about a further month or so, but eventually that stopped to, by perseverance and constantly putting her in the situations where she'd encounter them. Next it was trains, and main roads, even though she could handle cars in the locality, she wouldn't go up to the main road where there were trains, and lorries and cars all at once lol. This lasted a couple of months, now she doesn't bat an eyelid.
It doesn't happen overnight and you may start to think that you are never going to get your puppy used to traffic, but then one day they're like Millie - cars are so trivial she refuses to wait for them to pass if she wants to cross!