Is Earth old enough for DNA to evolve?

This bit isn't an important, but I thought I'd correct it in the interested of accuracy. Life on Earth is estimated to be almost twice as long as that. It's difficult to tell, because there aren't so many rocks remaining from the distant past to find traces of life in, and when the life you're looking for is simple, single-celled organisms, it's hard to identify exactly when you've found it. Clear evidence of microbes has been found from about 2.7 billion years ago, and controversial evidence goes as far back as 3.4 billion. The consensus is that the earliest life arose somewhere between 3 and 4 billion years ago.Now, on to some of the more important mistakes!Dr. Adequate already alluded to this, but you're framing this question all wrong. You seem to be thinking about only one organism having these mutations, but there is a lot more than one organism out there. To take one arbitrary example, one study of Lake Mendota in Wisconsion, estimated the density of heterotrophic bacteria to be between 300,000 and 3,000,000 per ml, depending on season. The volume of Lake Mendota is approximately 505 million cubic metres. Taking the lower range of bacterial density, that means about 151,500,000,000,000,000,000 bacteria in the lake.Now, in favourable conditions, some bacteria can produce a new generation in a few minutes, but even allowing for a much longer (arbitrarily chosen) average generation time of 12 hours, you're still talking about 606 trillion new bacteria produced every day. And each new bacterium will carry more than one mutation.This is why natural selection is important, despite your dismissal of it as taking too long. Natural selection is simply the process by which, out of the trillions and trillions of mutations that happen in this single lake every day, the deleterious ones are eliminated.Time doesn't look a problem to me, here.

I think this picture is badly put together. It is labelled as if the centre is the past, and left and right are the present, but that's not actually how it's drawn, since molluscs (snails, claims and octopuses) lie right in the middle at the four billion year ago mark. It's more accurate to think of the whole outer rim of the diagram as the present. This gives the impression that there is far more diversity around today than ever before, but that's just because, as the caveat on the bottom says, they've missed out most extinct organisms.As for whether we're undergoing another mass extinction, that's a matter of debate, but some would say yes. Here's wikipedia's article on it.

Point taken. I didn't see the dashed lines until you pointed them out. Maybe it's my the colours and resolution on my monitor, but they're very difficult to make out.