I'm not at all sure what Gayak's sentences 2-4 mean (since they seem to contradict his earlier definition and probably even themselves), but his first sentence clearly states that a supernatural being would not be a part of the universe and could not interact with it. With that definition, any insistence on a supernatural being that does interact with the universe directly contradicts that definition of supernatural being. So, a supernatural being interacting with the universe is a logical contradiction.
That's a reverse ontological argument: Supernatural beings are defined as beings which cannot interact with the physical universe? Of course the question arises, why would you define supernatural beings that way? Where does that limitation come from? I could just as easily define supernatural beings as beings which exist in all possible worlds. I'm sure no one would let that slide.
If that's what qayak has in mind, it still doesn't help him. I'll simply assert the possible existence of otherwordly beings, which exist outside of time and space, yet CAN interact with a physical universe and not be detected. We would then have a set of possible worlds where qayak's non-interfering supernatural beings exist and another set where interfering otherwordly beings exist. Since we don't know what set we belong to, qayak hasn't moved any closer to establishing the logical impossibility of a being existing outside the universe yet also interacts with it.
If that's what qayak had in mind, he would not have added the "easily detectable" part either.
Anybody tried to cross your toes lately? And did the subject "just happen" to have theirs crossed during the test? In street shoes?