i barely ever post. so i figure i'll just ad my 2cents here and there..
looking at both of them, it's pretty clear they've used artificial light. probably flash, cos i don't really know anyone who shoots with constant light. not for fashion anyway. Specific to both, the shadows are not hard. very soft. so both lit with a soft box, or at least bounced. Although the top picture is pixelated i can't really tell. but i assume i can see a slight shadow on their right hand side (our left) so there' definately direction. but not hard at all. just off center. the bottom there's little shadow at all. either it's filled in well (with secondry lights, or reflectors) or maybe they're using a ring flash.
For something grainy, unless you're shooting with film it doesn't apply to digital so much (it still does. just in different ways..) but the faster film you use, the larger the grain. With faster film, you need less light. either you have a huge depth of field, or like EletricAlyse said a medium format camera which depth of field is reduced as you move up to large formats. As for overexposed, like the first photo- looking at the highlights onthe face, i would assume it's makeup more than most. although possibly a hard flash/low powered, far away to bounce it back into camera to give that shine on their cheeks.
As for colour, there's not much to the first. but the second has been graded quite nicely. I bet it's all done in post, there could be filters on the camera but it seems quite selective so i wouldn't think so. same with having gels on the flash- it's more the shadows that are affected.
colouring shadows is possible. just more difficult to get right sometimes. so i assume it's done in post. if it is i think you jus thave to notice that overall the picture looks pretty cyan, if you have your monitor a little brighter you can see the blacks aren't black (not in the hair anyway) and are clearly a blue/purple colour. would also explain the lack of shadow and how it's quite deep in the corners compared to on her.
one thing i find important to know is learning how to add colour to your photos. if you can't push the colours you've already got overlaying ontop works quite nicely. esp. for colouring shadows and nothing else/selected areas.
that was a bit messy. but i hope it helps