The concept of prayer

To the greatness of the Gram Shlita,
Not long ago, I spoke to a counselor about a close friend who had crossed over to the 'other side'. I talked to him a lot in an attempt to understand what was bothering him.
I asked him to write it down, and I told him I would send it to you and we would be very happy if you responded to it,
I would be happy if you would review this letter and if you can, it would be very helpful if you could send him a response email.

Prayer
Assumption A:
God judges man with justice solely according to his actions = his choice. It is impossible for external factors to influence a man's choice of good or evil to affect his "reward and punishment." "Will God pervert judgment, and will the devil pervert justice?" (including the assumption that there is a worldly law).
Discount on:
God "hears" man's prayer for himself and for others, and prayer works in a specific way (apart from the psychological effects, etc.) to obtain the requested need.
This assumption can be based on many verses in the Bible, such as "And it came to pass that he called to me, and I heard him, for I am a wretched man" – regarding the poor man who prays for the afflicted – a man's prayer for his fellow man.
Likewise, "And the Lord heard their cry," "And God heard her," and many more.
And the Talmud is full of this matter, such as "By my mercy and my life," "The prayers of the righteous change the measures of the Blessed One" (Yevamot 67), as well as Ezekiel, and many others.
The assumptions seem contradictory.
If, according to the judgment of man for his actions, he does not deserve the desired need – how can we assume that prayer will help him?! Will prayer work against justice?!
And if we try to excuse ourselves and say:
A: Prayer makes a person better and after it, the desired need is fulfilled.
B: The person receives a reward for the very act of praying, and after that, the desired need is granted to him.
We reject this for 3 main reasons:
A: What is said about a person's prayer for his friend (which I proved above that according to a Bible verse, such a prayer also works), in which it is certain that the friend of the one praying will not become better and will not receive a reward for the prayer?!
B: If the person became better/received a reward for praying, the reward can come for anything, why do we assume that prayer will work specifically to achieve the desired need?!
C: There are many things besides prayer that make a person better/a person receives a reward for them, why didn't it say that a person will engage in Torah/morality and this will work to obtain the desired need?!
Regarding sky accounts
I can accept the answer "Heavenly calculations," when there is something I do not know that pertains to the matter. To Dog: (In Dog, I will simplify the abstract concepts of reward and justice for the unseen, to make the explanation easier).
A righteous person of a certain level whose reward = X. I don't have the ability to know how much reward he deserves (what his challenges are, etc.), so I won't ask why a certain thing happened to him, that's "heavenly calculations."
In our case, a righteous person at a level whose reward is X (indeed, it is unknown), and his friend prayed for him, we will define the need sought in prayer as Y reward. If the prayer is accepted, it turns out that the righteousness-reward equation is: X=X+Y, (as stated Y is equal to the requested need that was accepted) = incorrect equation. Instead: Xrighteousness=Xreward – the correct equation, justice.
Summary: In our case, there is no relevant data that is unknown, so here I do not accept the answer "heavenly accounts."
Regarding "mutual guarantee"
Some claim that the prayer's right/positive influence on the worshiper is imputed to the right of his companion and biases his judgment toward good – a person's prayer for his companion works to achieve what is desired, by virtue of the mutual guarantee between people.
This argument describes the phenomenon nicely, but does not at all justify it, and does not reconcile it with assumption A above.