No. But that is irrelevant. Effectivity is independent from tradition.
Hardly.
You suggested that a theist would get just as many "hits", under the assumption that what one believes about prayer, as well as what is being prayed
for, is entirely irrelevant to the effect it has on the one praying.
You, an atheist, would get as many hits from a glass of water as any God. As an agnostic polytheist, though I rarely pray, I can attest that praying to, or at least invoking, something that I actually believe has power, particularly one that's constantly reinforced through culture, has an influence on my behavior and confidence, making
me, in effect, the instrument of my own prayers' fulfillment, together with the rest of my culture. I'm not, and have never been, a monotheist, but I suspect the same psychology is going on.
It's probably one of the reasons why in some fantasy settings, Gods' powers is directly related to the number of worshipers they have. The authors of such works realized this phenomenon, either consciously or subconsciously.
Obviously the effectiveness does depend on
what one is praying for. No amount of prayer, to any God, water glass, or even Sun herself, is gonna make her reverse course, for instance.
By the way, do you think Apollo answered prayers, too?
Why are you asking about it in the past tense? He's still worshiped.