1.I think it's best not to have a bloodstone in your inventory when talking to him.
2.That way, you need to find the imp, which likely means that you will encounter him in Maradinos hideout, where you will also
3.find the bloodstone, eventually.
4.Then it's back to Frederic.

I don't know how the woman in the inn ties into the quest (if at all). Didn't get any response about her.

About the poisoned garden, I think that is just an alternative entrance to the villa.