This is my go-to site for chainmaille patterns. I found the steps easy to follow and there's a wide range of styles in a variety of difficulty levels.
Oh, awesome. I got really good at doing hair wraps for my friends when I was younger, but I can't for the life of me remember now exactly how I went about it... I think I generally used two or three colours and tied them on at the top, wrapped one strand of floss around for about an inch or so leaving the other strand(s) getting wrapped along with the hair, then swapped colours so I was then wrapping over the tail of the previous strand etc... and continued alternating like that... Definitely use embroidery thread though, and stringing beads on is always fun as well (glass e beads are probably best size wise). I don't remember if I braided the hair first or not, but it certainly wouldn't hurt, and keeping it damp is always a good idea as it does help make sure you don't end up with strands trying to poke through. I will say though that it is infinitely easier to do this for someone else than to try and wrap your own hair, so I'd suggest finding a friend who's also interested and then do each others.
As for exactly what you have in the image posted, Erica, I'm not sure if that's exactly the technique. It looks more like the beads are strung onto the hair directly, which I've also tried by doing a very fine braid, stringing on the beads and then wrapping (and kind of sewing through) the very bottom to keep the beads on. One warning I will give is that hair falls out. Eventually, all the hair in that braid will have reached the end of it's life, and you will end up with beads everywhere if you don't see it coming and remove them before hand. And yes, I did learn that one the hard way. >_< (This is particualry important with very fine braids as the less hair involved, the faster it'll happen).
Either way, best luck trying this out- it's a pretty awesome look. :)
You could also attach some bows to some of those safety pins, and then she could pin them to her purse/bag/etc... Or make a button bracelet/necklace, or fabric cuff, or something along those lines...
Perhaps a collection of hair bows in some of her favourite colours and/or to match some of her favourite outfits would be nice. Or a drawing of the two of you (or your group of friends) at your favourite place to hang out.
What kind of supplies do you have on hand?