I would think for the initial dates (if he was the one who did the asking out) he should pay, the fact that he isn't I would think means he's not really into her.

When I go on a date and I know in the middle of dinner that this isn't going anywhere I will make sure I pay my half. It's happened a few times and I pay my half just to make sure it wasn't like I went on the date for the free meal. I think taking turns is a really good practice after the initial few dates.

The "it's your money" guy- I'd have just shook my head, got up and left the restaurant without saying a word. Just tacky to say.