The logic of prayer

Hello Rabbi
Why would God, for example, want to heal a sick person specifically if someone prays for him if He would not heal him in any other way? If they did not pray for the sick person, is it "okay" from God's perspective not to heal him? If that sick person does not have relatives to pray for him, does he deserve to be healed less than someone who does have relatives?
Besides, what is the connection between intention and the effect of prayer? Why is it that if a person means more to his words, is there any reason why it will have more effect than a person who was thinking about something else at that moment?
As far as I understand, the questions are also relevant to your theory that prayer has no effect today because you claim (if I remember correctly) that prayer did work during the time of prophecy.