They didn't say, but the usual practice would be to use the usual geologic dating and apply that to things found in that stratum. If someone had actually buried the hatchet there, the hatchet might be of more recent origin, but if it had been lost in the mud it would act like an ordinary rock.
Tool typology. See my answer way back in post 19.
C14 is not very useful past about 50,000 years and completely useless on inorganic material (like stone), because it has no carbon.