Platonic small talk and then 0-100 asking her out. It doesn't need to be that abrupt or hyperformal. Also why does she seem "cool?" You're forcing rapport a bit rather than allowing HER to come to that conclusion because she's invested. There is no substitute for this really and even if you do get the number, there's a difference between a solid number and a flaky one.

That said, I don't think you're that far off. First, rather than asking several questions per message, I'd try to stick to one topic at a time until conversation really starts flowing. Also, let things breathe sometimes and leave space. Statements can drive conversation too. Indeed, this is what creates the kind of playful banter that really gets things going.