As far as the DL booking, yes that is fine. They won't care about any other bookings on other airlines. While open jaws on the EU end with a US origin is fine, DL (and other Skyteam carriers) do not allow open jaws on EU end with EU origin (unless origin and return are within the same country). For example GVA-JFK origin with JFK-BCN return would not be allowed to be booked on one ticket (you'd have to book as two one-ways). GVA-JFK with JFK-ZRH return would be allowed since GVA and ZRH are in the same country.