All three happened to me. Yes, when I married it was because my future wife (now ex-wife, though) who proposed to me. I was also asked out by a girl before. And when it comes to showing interest first, that is a toughie as quite often you do that without realizing you do that.
To be frank I can be rather shy when it comes to these things and that #metoo stuff even made me a bit scared. When it's the girl who takes the initiative I can at least be sure I did not "overplay my hand" with her, since if she would reject me when I asked her, she would not come to me first, would she?
Since I believe in an equal world or at least that is my own ideal, her initiatives to me should be the worth as much as mine to her. And I also don't see why she can't pay for my drinks, and I don't say this because I'd like to "profit" on her, as I would also pay drinks for her, but I mean, have things a bit in an equal setup.
When it comes to a relationship, I guess somebody has to take the initiative, but should men have the "privilege" to be one for that? I don't think so.