What are documented benefits of prayer?

A personal matter. Prayer can make you feel good inside. It is useful for believers as it allows for an external comfort for ones problems. Tests of prayer for specific outcomes have never proven better than random. So it is not used medically but can be used personally.
See cite. Please read: http://stason.Org/tularc/health/alternative-medicine/prayer-health-benefits.Html. Although the controls may not be as rigorous for studies involving prayer, they are none-the-less encouraging. The article cited above refers to studies regarding patients with cardiac problems as well as aids. It dicusses both personal & distance prayers.
Depends how you mean. Two sides to this. 1) Causality in prayer by its very nature is unprovable and therefore not documentable. Faith = belief w/o proof. 2) Prayer fulfils an emotional need for some people. The psychological benefits of prayer have been scientifically documented. Whether the object of prayer is real or not is immaterial. It's the act of prayer that effects the psychological benefits.