In regards to the greatness of tefillah, I would like to relate that I personally witnessed in my work for the tzedakah organization ‘Lachmei Mordechai’, which distributes food packages every week to widows and orphans in the city of Beit Shemesh. The leaders of the organization once asked an orphaned girl to say Perek Shira for forty days as a zechus for a bochur who was in need of a shidduch in exchange for a nice payment. On the 40th day, the girl called the organizers of Lachmei Mordechai and asked if the bochur was engaged yet. They answered that he was not. She then said that she had good news. On that day, her 40th day of saying Perek Shira, she had become a kallah. She said that she would now say Perek Shira for another 40 days, without any payment, for the benefit of the bochur.
We saw a clear fulfillment of the Gemara’s words (Bava Kama 92A) that when one davens for his friend while he is in need of the same thing, he will be answered first. In this story, she davened from the depths of her heart for someone else, but she received her yeshua first.
The truth is that it is very hard for a person to bring about his own salvation, as Chazal say (Brachos 5B) that a prisoner cannot free himself from jail. However, if one davens for someone else, it is easier to arouse Divine mercy for oneself. This is because Hashem says: If a human being has mercy on his friend, I certainly should have mercy on him.