When I hold the door open for a lady, it's just being polite and she shouldn't read much into it. I hold the door open for a lot of people. When people hold the door open for me, I appreciate it. I stand up when a lady enters the room in some social situations. In some situations, I wait for the ladies to sit at the table and help the nearest one with her chair. I walk on the street side on the sidewalk. A lot of these are throwbacks to a different time, but they are polite in our society.
I feel it's fine when my date wants to pay. My general rule is if you ask them, be prepared to pay, for everything. When you take a girl out, you don't head up to the parking spot after the movie, you ask her if she wants to eat, and you pay. If she insists on paying for some of it, that's fine. Same thing for the ladies. If you ask him out, be prepared to pay, for everything. If he is a gentleman, he'll insist on paying at least for some of it, and that's fine. But don't expect it. Once you get to know each other a lot better, then you can haggle about the check.
Your guys' whole argument about "what if she's killing you" isn't a valid point at all. There's a difference between respect for women and just being stupid.