Russell's paradox is a famous theorem in set theory. It asserts that "the collection of all sets is not a set itself". In the other words "the set of all sets doesn't exist" in the world which ZFC axiomatic system describes. Note that sets are the only legitimated objects in ZFC system. So in the ZFC point of view the collection of all sets is not an object in the realm of existence.
Russell's proof for this theorem uses the self-reference of the notion of "the set of all sets". Also I think this is a formal form of the famous discussion for non-existence of God which is a self-reference notion itself. For example according to the usual definition of God, he is an eternal immortal being with unlimited power to do everything. But he can annihilate itself by his unlimited power too so he is mortal, a contradiction. This fact shows one should restrict the properties of God in the definition in order to avoid self references and contradictions.
Question 1: Did Russell mention the above correspondence between the problem of existence of the set of all sets in set theory universe and the problem of existence of God in the real universe in his works explicitly or implicitly?
Question 2: What are the philosophical impacts of Russell's paradox as a theorem of set theory on the problem of existence of God in theology?