I now delve into the pressing issues on my mind. I've heard people talk about their "relationship" with God my whole life. I've even talked about mine in front of crowds of encouraging, wishful thinking friends, and describing how God had "answered" my prayers. If concepts were software, this one would be vaporware. Enter the cold hard voice of reason. I will attempt to distill the various ramblings of people I have tried to talk to about this.

Let's say you pray that God would help you find a better job, or whatever. Most Christians would hold that all of the following could constitute an answer to that prayer.
a. You hear a voice that says Yes or No.
b. You hear and sense nothing.
c. Absolutely any one of the items in the very large set called "all possible events" happens, including losing your job and getting crushed by truck or becoming a Satanist.

"God will answer my prayer" means "Anything at all might happen." Conversely, the set of circumstances most Christians would describe as non-answers to prayer is actually the null set. A friend of mine recently admitted
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I agree with your points that there is no way to know whether God answered a prayer or it just occurred through "circumstances."
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This is like a pen pal that you've never seen and never receive a response from. Maybe their letters are getting lost in the mail, maybe they aren't writing, or maybe they don't even exist. Either way, what you have is definitely not communication.

Let's understand something very basic. Meaningful statements about reality must exclude certain possibilities (they must define a non-empty partial subset of all conceivable possibilities.) A statement that is true in any imaginable state of affairs is meaningless. This of course is the beauty of so many religious concepts. As long as you don't think too hard, you can believe them no matter what, and that is a comforting thought.