It is relevant, as it says something about the god you worship, and the many excuses you must constantly come up with for him.
ncbi.nlm.nih.gov/pubmed/16569567
Here is a good example
A Randomized, Controlled Trial of the Effects of Remote, Intercessory Prayer on Outcomes in Patients Admitted to the Coronary Care Unit
William S. Harris, PhD; Manohar Gowda, MD; Jerry W. Kolb, MDiv; Christopher P. Strychacz, PhD; James L. Vacek, MD; Philip G. Jones, MS; Alan Forker, MD; James H. O’Keefe, MD; Ben D. McCallister, MD
Arch Intern Med. 1999;159:2273-2278.
This, for example, the authors did their calculations wrong by making 34 separate t-tests and not accounting for that, and thus came up with incorrect results.
Hardly, it trashes your silly argument that some third partying observing.
It doesn’t effect the possibility of studying it, only the practicality. Are you suggesting that god only answers prayers once every thousand years?
Irrelevant
Following evidence is not faith. Now you’re just being silly. You shouldn’t put your faith in anything that claims to have absolute answers. No one has absolute answers. People who claim to have absolute answers are just liars.

Refresh my memory. What’s your proof that some prayers are answered positively?