You mention gender role stereotypes but then fall prey to one when you clearly think you should be served first because of your gender. If you don’t believe in equality and would rather stick to ancient and out of date traditions that’s fine but perhaps he is a bit more progressive and you are not well suited to each other.
It’s ok for a woman to pay, it’s ok for a woman to suggest a second venue, it’s ok for a woman to make the first move. It’s not 1950 any more.
Regardless, like others have mentioned, having this much to question after one date isn’t a good sign.
Sounds like textbook NPD, particularly his backstory.