the white is called the "free edge". It isn't that the nail is dead (I think nail is a bit like hair, actually, it grows out through the cutical the way hair grows out through the follicle). The free edge is just the part of the nail that isn't attached to your finger. When your nails get long its bound to happen!
The first thing you want to do is figure out what kind of shaped nails you want to have. The following link is about fake nails - but it has some nice illustrations.
http://www.fingernailfixer.com/enhancements.html
(I like a hybrid cross between the 2nd and the 4th)
Nobody has perfectly symmetrical nails. The cuticles of different nails can be a slightly different shape. Basically... You want the nails to be fairly much the same shape to try and help them look more symmetrical.
Squoval (squarish with rounded corners) is fairly popular. When you cut them I'd try and cut them fairly flat but maybe try and shape the corner a little. Then tidy it up with a nailfile.
There are lots of handy hints on how to do all that via google...
The following link is a "french manicure" which is a natural look that is deceptively hard to get right... Notice the free edge. White nail polish on the free edge to make it whiter and a pink / beige on the rest. Hard to get the line between the free edge and the rest looking tidy...
http://www.beautyden.com/frenchmanicure.shtml
Over time the nail will stay attached to the finger higher up the finger. That way... You will be able to grow them longer without them weakening too much. After a while they do get annoying, though. Hard to do things...
http://www.soyouwanna.com/site/syws/...manicure2.html