How does carbon dating enter into the discussions about the Christian views of creation?

Evolution continues with its assumptions about the age of the earth in large part because evolutionists are proceeding from a desire to be able to invalidate the Bible. If the Bible can be invalidated, then the concept of God can be invalidated. If all we have and are is a complete product of natural processes, then “God is out of a job,” and He is no longer necessary. It is the alternative that is scary to an evolutionist, and maybe never expressed better than by British philosopher Bertrand Russell (an avowed atheist whose daughter ironically is a born-again believer). He said (to paraphrase), “I don’t want there to be a Supreme Being. If there is a Supreme Being, I owe Him; I must answer to Him. I don’t want to have to answer to anybody for my beliefs or my lifestyle choices.” That being said, the idea has always been that, if the earth is 4.5 billion years old, that somehow provides the basis for the legitimacy of evolution by providing a chronological platform that would accommodate the timeframes necessary for evolution to accomplish itself. An unfortunate byproduct of that has been to attack the age of the earth suggested by James Ussher (1581-1656), the Anglican archbishop of Ireland, who suggested that, based on Biblical chronologies, the earth came into being in approximately 4004 BC—around 6:00 pm, October 22, 4004 BC, to be precise. Ussher was actually a man of magnificent scholarship who, despite his questionable methodology, remains a hero of sorts of “young-earth creationists.”
Actually, the problem with Carbon-14 dating is that it is flawed in three ways because of the assumptions the scientists who promote it have made, and those assumptions are: (1) that the initial conditions of the rock sample are accurately known, (2) the amount of initial or resulting elements in a sample has not been altered by processes other than radioactive decay, and (3) the decay rate of the original isotope has remained constant since the rock was formed. If the assumptions are wrong, then any conclusions based on those assumptions are likewise going to be in error. Fundamentally, while using scientific method in the present, there are also assumptions about past historical events regarding the rock of which we can only assume. Because of this, we cannot objectively directly measure the age of anything. To understand this better, let’s take the example of an hourglass, with sand pouring into the bottom and still remaining in the top. Now we could measure how fast the sand is falling and how much sand is already in the bottom of the hourglass to compute how much time has passed since the glass was turned over, and these would be correct from an observational standpoint, but the conclusions could still be wrong. They would be wrong based upon three assumptions we would be making: (1) was there any sand in the bottom of the hourglass when it was first turned over (what were the initial conditions), (2) had any sand been removed from the hourglass (obviously impossible if the hourglass was sealed), and (3) was the sand falling at a constant rate. Our ultimate answer is completed wedded to our assumptions. If our assumptions are wrong, there is no way our final answer can be right. In the same way, because of errant assumptions (including historical science which can never be observed), the conclusions for the age of the earth based upon Carbon-14 dating must be viewed as incorrect.