I would argue that it seems to bring some level of comfort for the person who's praying, and I tend to believe it has something very much to do with the biology of our brains. I think there is a natural high that one gets from it. I prayed at times when I was suffering from anxiety and existential fear in my mid-teen years, and it did... something. Not something I can quantify and it's not something that solved anything for me. A fleeting moment, but I was not thinking straight at the time so I could never replicate it now and tell you what it felt like. It's a strange thing and it's one act that only human beings engage in and I find the effects it has to be an interesting part of human psychology.
That said, I do not think we should be praying for a solution to a problem in lieu of action to solve said problem. In conjunction with? Whatever floats your boat.
Meditation and/or a deep state prayer have been shown to increase your serotonin and dopamine levels.
I thought so, but I hadn't done too much research on it.