Carbon 14 has a half-life, which means that after a certain time, half of it will be gone. After that time again, half of WHAT'S LEFT will be gone, i.e. a quarter of what you had originally. After 3 half lifes, you will have an eighth of what you had originally.
So given that the amount of C-14 in a body is constant, then Carbon dating is an accurate method of determining how long ago it is since the sample died, a. The half life of Carbon 14 doesn't "fluctuate" over time like you seem to be suggesting. It is a constant, physical thing - it isn't affected by temperature, pressure, biology, climate change, etc etc.... It can't be changed, it will always be the same! The only way in which it might not be accurate is if you can't obtain a big enough sample to observe a measurable amount of carbon-14 in. But with modern spectroscopy methods the precision they can measure very small amounts is very good.