If anyone can answer this or discuss it please do so.

Shooting stars happen at night and are recognizable by their little jingle that they give. I was told to open my menu screen the moment that happens. If anyone knows what'll happen, please explain it to me. Also, you can discuss your experiences with shooting stars here f anything happens.

I don't know why you would open your menu screen.
When you see one and you have nothing in your character's hands, tap your character or hit A. Your character goes into a "praying" pose. The next day you get a gift from Wishy.

Thanks CheesGirl, I'd always wondered what the point of them was. :D Now I know.

What kind of gift? Furniture or something?

Usually a semi-rare item, like a spotlight item so yeah, furniture. There's a certain painting that he might give you also.