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For example, do two galaxies situated in proximity reduce the atom decay rate in each other?

What happens with decay quanta escaped to infinity? Does the radius of apparent horizon effect the lifetime of the atoms in the universe?

Do atoms placed on a planet's surface decay slower than those placed at a distance from the planet? Is this decay slowing equivalent to the time slowing due to general relativity? Is it affected only be the mass of the nearby object or by dielectric constant of the material?

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The quantum Zeno effect occurs when the effect of some interaction is to produce a slower version of the wavefunction evolution that would have occurred in the absence of the interaction. It is not specifically about "observers", and it requires interactions which specifically have a "freezing" or "restoring" effect on the quantum state. For example,… mentions repeated applications of ultraviolet pulses to a collection of ions, which reduced the amplitude for the ions to enter an excited state... – Mitchell Porter Dec 22 '12 at 6:41
So the answer to your question is that, probably there is an astrophysical environment somewhere in which there are interactions occurring with a similar net effect. But the subtext of your question seems to be that the QZE has to do with the presence of observers, and that's not what it's about. – Mitchell Porter Dec 22 '12 at 6:42
@Mitchell Porter can you please clarify what you do not like with this question? I never mentioned observers... – Anixx Dec 22 '12 at 7:01
It doesn't mention observers, but it looks like it was motivated by the idea that it's specifically observers that cause the QZE. Otherwise I don't know why you would imagine e.g. that one galaxy reduces decay rates in its neighbor. – Mitchell Porter Dec 22 '12 at 11:43
@Mitchell Porter so your poit of view is that a galaxy will not affect atom decay rate in another galaxy? – Anixx Dec 22 '12 at 13:34

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