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.
Yes it does. Note that it's meditation and prayer, prayer being a form of self meditation and that the effects are the same regardless of who (which god) is being prayed
to. The evidence is that prayer benefits the person praying, but not the person prayed for.