Vaeschanan - Having Visions Fulfilled

What is the concept of the two names of Hashem - Yud-Kei-Vav-Kei and Elokim - that are invoked by both Avraham and Moshe? Why is Avraham's request to be the forebear of Priests and Kings fulfilled, while Moshe's identical request is denied? What is behind the request of both Avraham as well as King David to 'not have kids' unless they will be appropriate servants of Hashem? What is the proper approach to asking Hashem to fulfill our requests and bring our dreams and visions to reality?