I'm interested that you think that science can't explain various parts of human behaviour in meaningful way. Brain science is still quite young and there is a long way to go so I'd say it was far too soon to be something that can be dismissed and used as an explanation for anything else. After all, Lord Kelvin at the end of the 19th century, a leading physicist of his day still have no idea how the sun could go on burning for so long and, who knows, probably someone was saying that because science can't explain it, god must be keeping the sun burning! I think it is important to realise that just because a properly thought out and researched explanation of something is not forthcoming now, is not an excuse to say that this lack indicates that god-did-it!
Actually I suspect there is some explanation of the various traits of human behaviour available. After all, the ones you mention are all to do with forming societies and making them run smoothly. Members who had some of these traits would be more likely to breed and pass on their genes than ones who did not. I'll look up some proper science on this but I don't think we can dismiss evolution so easily and, of course, claims that people were created by an unknown god would need some evidence too so just because we haven't got a full explanation does let a creation event in for free.
Now the thing with prayer is that there are, in essense, two sorts -
1. Prayers that are directed to a deity by and individual and a response asked for to that person.In effect this all takes place in a the person's head and even if he claims to get an answer to his prayer, there is no way to investigate if claims are true.
2. Prayers in which something is asked of a deity in which some external action is asked. These could be healing prayers but might include a whole lot of other things. With this prayer type we can look to see if the prayer is answered by monitoring the recipient.
Now I have no doubt that you hold the type 1 prayers to be very important to you. After all, they are about a relationship which is personal to you so of source you value them. the thing is, though, that even you cannot distinguish between a deity speaking to you in your thoughts and your subconscious coming up with answers to problems you pray about and these answers popping into your conscious mind after you have prayed your prayer. For obvious reasons, you prefer the first possibility but, I suggest, you cannot rule out the second one.
Prayers of type 2 offer us a chance to glimpse into the possibility of the efficacy of prayer. now we know form experience that prayer doesn't work every time. If that were the case, there would be no need for children's hospitals since surely parents pray for their ill children. So what we see in practice is that the only way to examine this is by a large study and to compile the results and see if a control group does as well as a prayed for group.
The best study in this line was the Mayo Study
In this study, patients who were prayed for did less well that those who were not prayed for. The thing is, though, that according ot the gospels, Jesus told his disciples that they could ask for what they needed and god would grant their requests. Jesus didn't edge around this with 'if it's god's will' or anything like that - it was a simple 'ask and you will receive'. So we have to ask, why was it that all the prayed for group got better quicker and without any complications? Did god have trouble with the volume of work for example? The fact is that although religious people say prayer works, the evidence of it is hard to come by. After all, people tend to forget the times when it didn't work and just mention the times when it did. Yet if Jesus was right, pray should work all the time and, ideally, amputee would recover their limbs like amphibians can.