If you’re worried about authenticity, probably compare notes with native cooks, but more importantly, check to see if the ingredients are correct. Very easy to get bastardised ingredients; as an example, living in an Asian country, I used to have a hell of a time getting the right herbs and vegetables for doing certain Western dishes with, and very common to get some pre-packaged “mix” of herbs instead.
Kinda, but nowadays it’s all filtered in so even in a mass market supermarket you can get some decent ingredients. Like anything else not common to the local palate, you have to pay. Kale is ridiculously expensive, for example.