The problem is that it's inappropriate to express interest if you're in a position of power over someone, whether you're a man or a woman. I think you were saying that, but point #1 lacks that context.
Make an introduction. Make your mild/budding interest in them clear enough. Ask them to do something that's clearly not work with you.
"Hey, want to get coffee sometime this weekend?"
You'll find out if there's preliminary interest or not. If they're interested but busy, they'll figure out how to make that distinction clear. If "sorry; I'm busy" is the entire answer, just assume they're not interested. You get one "free" chance here; make it fairly clear that you're interested; don't invite them out for a "team dinner" and then arrange for the rest of the team to not show up or other chicanery.
Personally, I've stopped ever pursuing anyone who works in the same industry due to the potential for weird dynamics, but it's sometimes not as cut-and-dry as people make it sound. Like the example with Chris Sacca, is flirting with someone at a conference a form of sexual harassment?
I'd not go with a co-worker that I have power on (like being the direct manager, or the VC). I can see many ways where the relationship can go awfully wrong.
I have eye contact and smiling with lots of people. It's just being friendly.