If I've invited someone to go out, I pay. Once the relationship is established then maybe, though not usually. On a first date if she insisted on paying with too much stridency I'd worry that there may be some sort of underlying issue.

It depends...Though there are some dates where I'm like no babe tonight's all on me. Granted there's gota be a good mixture of that on both sides.

It depends on who it is... but generally, first date, I open my purse. I also insist on paying if I asked... but rarely get to complete my offer without adamant protest.
If I was dating a woman I would always split unless agreed upon as a "treat date" otherwise.
I just offered up a treat date, this evening... we'll see.

Typically the one who extends the invitation should pay, but if paying separately is mutually agreed upon before the date, that should also be acceptable. That being said, if a man who wants a relationship with me has far more wealth than I do and still wants me to always pay my own way, the opinion I form about him probably won't be all that conducive.

I will always offer to cover the bill, but I will also do what the other person is most comfortable with.

Yes.