My question concerns on of the laws of נוח. What exactly are the conditions in which food becomes offered to pagan idols? Does the responsibility of making it an offering to whom or what fall on the shoulders of the person or persons hosting the meal? If this is so what makes the determination in a public setting like a restaurant? If it isn't so how does one determine whether or not food has been offered to idols? Or are we just not ever supposed to eat with people who are outside the faith? As always, תודה רבה for your time!

That's covered in our Khav•rutꞋ â. I'm sure you'll get to it soon. In the meantime, the most prolific problem is if a Christian (viz., one who believes in the divinity of Jzeus and/or in the New Testament) says a blessing over the food, which constitutes the Διαθηκη Καινη (NT) term τεθυμενα (tethumena; "idolatrization"; see The Netzarim Reconstruction of Hebrew Matityahu (NHM) note 22.4.2).