That's a lot of questions, which I'll more or less handle in stages.
"How much do we know about the accuracy of carbon dating? Are there things that could affect the accuracy of carbon dating when applying it to find out the age of a fossil?"
I'm not much of an expert on this, but typical carbon dating reports include standard error bars, usually too small to be very important for evolution. Some problems outside the error bars occur if there's some contamination of the sample. Calibrating errors due to climate effects is an ongoing effort, but again not a big problem for most purposes.
More importantly, I doubt if carbon dating is really what you're interested in at all for most evolutionary dating, since it only works for relatively recent dates, because of the short half-life of carbon 14. A variety of other radioisotope methods work for longer times, extending over the whole age of the Earth. Those other methods are generally even more reliable, when used for the proper time scale, because they involve fewer biological complications. When several different isotope dating techniques give the same result, that result is very highly reliable. But you should check more detailed other sites for more comprehensive descriptions. Real science sites include http://www.gpc.edu/~fbuls/ast101/part2/radage.htm
. Most of the sites that turn up in Google are amateur creationist rants.
"Also, by evolution, you do mean a frequent number of small changes over generations, resulting in the seeming evolution of one species to a completely different one?"
Yes, except minus the word 'seeming'. Of course evolution also includes smaller changes that do not rise to the level of new species, and larger changes that give rise to different kingdoms, phyla, etc.
"Also where would the line be drawn between a species and another that has evolved from it." Good question. If there's just one interbreeding population, the line is arbitrary, a matter mostly of taste. If a population splits into two or more separate groups, we say they form separate species when it becomes hard for them to interbreed. That line isn't perfectly sharp, but it's clear enough. If one of the groups closely resembles the ancestors, then we say the other group or groups are the 'new' species.
"Also how would you define a hybrid(ex: mule)? would you claim it was the evolved state of two species?"
Who cares what names we call the poor mule? This is not about names but about finding a real description of what actually happens. We know what the mule is- a horse-donkey hybrid. Since mules are almost always sterile, they play no role in the future evolution of donkeys and horses, and we say that donkeys and horses are separate species.
(published on 10/22/2007)