"When is it appropriate to go Dutch?"
Is this Q about in a relationship?
About the second Q:
This is actually somewhat culturally related.
Here in China, many guys would pay for girls (whether in a romantic relationship or just friends) even they actually don't really want to, since paying for girls shows that you're not a stingy guy. It's a tradition. Some girls would complain if their boyfriends would just go Dutch, others don't. So, it depends.
In the U.S., asI learned, if a guy asks a girl out, he should pay. Who asks the part out, who pays.
In North Europe, they usually go Dutch (due to the feminism).
I personally prefer going Dutch. I have no problem with it, I would even pay for him.