How can I keep that side-curl still?!

The second one looks like the underlayer of the bangs (the part inside the big poof) is teased, then hairsprayed, then the layer on top (the smooth bangs you see on top of the big poof) is then combed over the teased mess, and either just sprayed in place or pinned down behind the bangs area so the pin is hidden, then sprayed.

I can't see the first one that well because of the glare, but it looks like a chunk of hair is just swooped into a curl right?  You could do that by gooping up your hair with gel (careful not to overdo it, but you would need kind of a lot), then after its dry, brush it out and shape into the curl, then spray with hairspray (holding the spray far from your head so you don't get a wet look).  You may need to do 2 coats of spray.  It'll be stiff, but it should stay.  Some bobby pins in the underside of it would help hold it too.  Don't touch it when its wet though or it will look wet, only after its dry.

I'm not sure what you're going for in the third pic, the curls in the back?  I'm not sure, but the hair is likely put in an ponytail in the back, then bobby pins are used to hold the curls in place (can be tricky to do it such that the bobby pins are hidden).