I want to say that "carbon dating is a form of chemical romance," but I suppose I should control my urge toward frivolous wordplay.
What I know is that the process involves determining the amounts of isotopes of radioactive carbon present in a sample of carbonaceous material. (Normal carbon in living beings has a small but consistent amount of these isotopes--C13 and C14. Very ancient fossil carbon does not.)
Since the rate at which these isotopes decay is fixed, the relative abundances of stable Carbon-12 and radioactive C-13 and C-14 let you figure out mathematically how long it must have been since the creature lived. Practically, it's mostly C14 that is the object of carbon dating.
As to how it has been validated, it's basically by cross-comparison with other knowledge. For instance, an early validation test was to carbon-date an ancient Egyptian barge whose age was known from the historical record.
Most of your other questions are answered here:
The main one that isn't, I think, is #1. I think the best short answer to that is that there are a great many carbon dating machines, and they are the property of the labs that use them.