More like police, or, really, guardsmen might be a better term for them, seeing as they are our main line of defense against dark magic. I suppose you could consider them soldiers, yes, though they technically aren't an army. My older brother works as an Auror, actually.

The making of them rather depends on the one making them. And most wand crafters, as far as I know, keep their secrets when it comes to their craft. But yes, they use wood, and a part of a creature, such as a dragon heartstring, the hair of a unicorn, or a phoenix feather. Picking out a wand is quite the process, especially since most witches and wizards do it as they're about to leave for school.

They are indeed. Among...many other things. [Which is the most polite way Newt can think to put it.]

Well. Some of us can change into animals. But that is a powerful magic that requires time and effort. There are various repelling charms and other, more simple disguises.