Was this the first time it made you throw up? The oats and whole milk make that a pretty substantial shake, especially if you just had breakfast an hour before. It could just be too much "stuff" in your stomach.
Not sure what you're asking. What use is a pre-workout meal? It gives you calories and energy to "use" during the workout. Useful if you're bulking or training for strength, not so useful if you're trying to burn fat.
Shakes are sometime used instead of whole food because they usually digest faster, unless they're loaded with fat and fiber (like, um, from whole milk and oats). That's one benefit of whey over other protein sources, the faster digestion/absorption.
That's an individual thing. I know people who can finish chewing a sandwich as they're gripping the bar, and I know people who can't eat two hours pre-workout or else they yak.
I'd try it for a while, adding at least some of the shake's calories to your breakfast. If you want, have something a little lighter an hour pre-workout, maybe just the half-banana and whey in water. But a lot of it depends on your goals (hypertrophy, fat loss, etc.)