If they dug up some person who was buried a couple of hundred years ago and could get a DNA sample, would it be possible to tell whether I am related to him or her?

At most, they could tell you that you share a relation to the corps. DNA is pretty definitive. Whether or not the deceased is the same person as the headstone implicates is subject to more scrutiny than DNA results.

but I’m no scientist.

yes. gross.

This is a really cool side of science. In Madagascar, scientists have found subfossil lemurs (lemurs that are several thousand years old and have not yet fossilized) and have been able to extract aDNA (ancient DNA). From this they have been able to determine who the closest living relatives are to these extinct lemurs. Pretty cool stuff, but doesn’t always work so well.

yes through mitrocodrial evidence.

Mitochondrial DNA is only passed down through the mother, so if it’s a male relative, no dice.