Not necessarily true, I've never been conventionally attractive, but I've had women approach me multiple times, in fact all but one (out of... 6 I guess) of my long term relationships were initiated by the woman... Of course that was when I was young, now I'm 50 and going through a divorce, I'm not holding my breath...
If she says no it doesn't come without consequences. You can't talk to her anymore without it being awkward, and if she's part of a larger friend group you're in the embarrassment is even worse.
You're overthinking it. I know because I do the same. But realistically most women are quite relieved when you can take a kind "no" in stride because the bar is so low in this regard.
If you accept rejection with dignity, it's not that big a deal. Don't be a creeper. It's not that embarrassing. And if your friend group is cruel about it, that's good to know. They'd be assholes in that case, and you probably want to find out they're assholes in a low stakes situation.
If you've asked in a friendly way, without putting stress on her, and accepted the 'no' without making a fuss and in the same friendly way, it doesn't tend to cause difficulty in my experience.
Nobody has to ask anyone out, its not compulsory. Women do ask potential dates out, so do men. Its pretty irrelevant who the one doing the asking is - the point is not to put the onus on one gender but that if you - whoever you are - don't ask, then you'll never know.
Exactly. I'm a dude and my SO all but asked me out (asked for my number and whatnot). At some point someone needs to take initiative, and the sooner that happens, the better it is for everyone, so it might as well be you, regardless of your gender.