1. Rashba cites Rav Hai Gaon that the explanation is that Hashem was teaching us how to daven. This is based upon the Gemora Rosh Hashanah that Hashem taught Moshe how to utilize the Thirteen Attributes of Mercy. (Mishmeres Moed explains that when the verse states, "Beis tefilosi," it is Hashem's house of prayer, where He teaches us how to daven.
  2. Rashba asks that it doesn't fit into the language of the Gemora when it says, "What does Hashem daven"?
  3. Rashba explains it to mean that it his Hashem's will that we should raise our level of observance in mitzvos (Rav Elyashiv) in order that the Midas HaRachamim of Hashem will overpower the Midas HaDin.
  4. Razei Brocha cites Rav Shamshon Refoel Hirsch that tefillah and tefilllin have the same root. They both mean attachment. We daven and wear tefillin in order to cleave to Hashem. Hashem also wears tefillin and davens in order that we should be attached to Him.
  5. The brocha of a common person and certainly the brocha of a tzaddik brings about blessing.
  6. Look at Chinuch 231 and 235.
  7. The source for kvitlech to a Rebbe can be from Ramban in Bamidbar 1:45.
  8. Yalkut Shimoni in Rus 3 stresses the significance of a tzaddik's brocha.