As for God and then the angel, why the switch in roles or persons: The Lord as we know has spoken on several occasions to the Old Testament patriarchs as well as a number of occasions in the New Testament. At times the writer "inserts" us into an account where God is already speaking to someone and we are not given the details of the initiation, whether God is speaking through an angelic agent or face to face. In this passage, all we know is that God personally starts a conversation with Abraham and what he must do to test (prove) his faith. Will he be willing to sacrifice his only gendered (begotten) son?
I think we can generally accept the action of the angel to speak and thus stay Abraham's hand as if it were God Himself doing the talking and intervention. Angels as their name implies are, among their other duties, messengers of the Lord and we find them often received by the hearers as if they were the Lord Himself. At times, the Bible clarifies their identity for us and at other times we are to understand that for all intents and purposes, it is God personally.
Keep in mind that no man has ever seen God at any time (Moses was placed in the crevice of rock only to view the hind-parts of God as he passed in His glory. Perhaps the full brightness of His glory could have killed Moses.
This could be a reason why God uses angels to speak to the prophets, etc. because his personal appearance might be too overwhelming for humans to endure in the flesh.
There has been some discussion that the three visitors to Abraham might have been two angels and the pre-incarnate Christ (christophenes). They appeared to Abraham as three strangers journeying somewhere and he was able to welcome, feed and walk with them since they exhibited human-like appearance (for Abraham's sake). Notice that two of them split off (angels heading to rescue Lot and family?) and one (the Lord Himself) stays to converse with Abraham. (Genesis 18).
I generally feel it is not critical or crucial when it appears that God interchanges His conversation or dealings with man between an apparently personal appearance and the appearance of an angel. At least, context and internal evidence of scripture usually inform us as to whether God is speaking or an angel has been sent on His behalf and the interchange of the two as in the passage you first discussed are not critical. From our point of view (and Abraham's) God was dealing personally with Abraham in either instance (direct conversation and the intervention of an angel).
Angels seem willing to volunteer the information that they are messengers and not God Himself, as they reject direct worship.
