How accurate are radiometric dating methods
There are about two dozen decay pairs used for dating.
Uranium 235 decay to lead has a half-life of 713 million years, so it is well suited to dating the universe.
Every few years, new geologic time scales are published, providing the latest dates for major time lines.
Older dates may change by a few million years up and down, but younger dates are stable.
Methods are precise insofar as they are properly used.
A good explanation of all of the dating methods used for samples up to about 200,000 years old, together with their accuracies and references to the scientific literature is contained in  Walker, Mike, "Quaternary Dating Methods," John Wiley & Sons, 2005
When the carbon dioxide, containing C14 as well as stable C12 and C13, is taken in by plants it is no longer exposed to the intense cosmic ray bombardment in the upper atmosphere, so the carbon 14 isotope decays without being replenished.
Radiometric dating is the method for establishing the age of objects by measuring the levels of radioisotopes in the sample. It decays to nitrogen 14 with a half life of 5730 years.
Carbon 14 is created by cosmic rays in the upper atmosphere.
Other methods do not require knowing the initial quantities.
For example, potassium decays into two different isotopes of argon having different half-lives.