Lost at Hogwarts Network Community

One of the students I believe are called first years dropped her wand which I almost stepped on. When I reached down to pick it up for her, the wand sort of leapt into my hand when I almost had it in my grasp. Do wands usually behave like this?

Any of you locals have recommendations for books to look into as a starting point for learning this world's history and customs? Because that library is gloriously fucking huge and I want to make sure I've got the basics before I go more in-depth.

And I have to ask, what exactly are the winged dragon-horse things pulling the carriages?