The reason why we can determine the half-life period of carbon-14 is because we have sensitive instruments which can measure the amounts of the material to a high degree of accuracy. Since we know that the half-life of an isotope is always constant, we can observe the change in measurements over a period of time to determine the rate of decay for the isotope in question. The longer we study an isotope, the more accurate our readings can get. There is fair reason why this method is used and taught in biology and chemistry books alike. Carbon dating is not useful past a certain point, of course, when traces become small. This point is at ~50,000 years. More information can be found here and here.
The thing about radiocarbon dating is that it assumes that a certain amount of carbon-14 was present at said time. With how flexible the atmosphere is, radiocarbon dating is based off of a loose variable.
As for natural selection, it's a means to an end which isn't necessarily the true answer, but the evidence is fairly convincing. It is, however, fairly ludicrous to deny the existence of evolution, in short, the idea that life changes overtime. The shortest and most compelling evidence is simply the pattern of fossilised life we can find in different layers of the Earth's crust.
I do not deny the existence and supporting evidence of micro-evolution. Adaptation and minor mutations exist—that is undeniable. Furthermore, the most compelling evidence in this area is undermined by findings of polystratic fossils.
Darwinism has nothing to do with that.
I'm not sure what you're trying to address.
So stuff can't be scientifically proven but religious beliefs can?
I have no idea from where you got the idea that I said or implied that religious beliefs could be proven and science not. My belief is that pursuit of answers that seek to satisfy questions approaching philosophical nature is unsuitable in the realm of science. An question such as "What is the meaning of life?" is never meant to be answered by science because the only answer that is true is true to the individual who answers it for themselves. Life might mean one thing for me, and a different thing for you. Does it mean the other is wrong? No. It's a purely philosophical question, and its answer is philosophical in nature.
When addressing the concept of philosophy, philosophy serves to lend solutions to questions that cannot be answered by science. Philosophy is about beliefs, and beliefs are surrounded by holding faith in the credibility of an event. The belief that distilled water will not burn is not faith, as it is fact that it will not burn. However, when criticizing evolution in a purely scientific manner and pointing out its flaws as a scientific claim, many of its most fervent defenders claim after numerous holes have been found is "evolution is factual," which is a conclusion that has been derived from ill-founded ideas. Creationism is the same way. It does not stand as a complete scientific fact. Both creationism and evolutionary theory (regarding the origin of the species and long term development of life) require a fair amount of faith in what credibility they have in order to regard either as fact. That is why both realms, as I believe, are ill-suited to the field of science.
