Avraham's Guests – Angels or Men?

Introduction

A Missing Revelation

Chapter 18 opens with Hashem appearing to Avraham:

EN/HEע/E
(א) וַיֵּרָא אֵלָיו ה' בְּאֵלֹנֵי מַמְרֵא וְהוּא יֹשֵׁב פֶּתַח הָאֹהֶל כְּחֹם הַיּוֹם.

Surprisingly, though, instead of sharing what Hashem then said to Avraham,1 the following verses proceed to tell the reader how three guests visited Avraham.2 

EN/HEע/E
(ב) וַיִּשָּׂא עֵינָיו וַיַּרְא וְהִנֵּה שְׁלֹשָׁה אֲנָשִׁים נִצָּבִים עָלָיו וַיַּרְא וַיָּרָץ לִקְרָאתָם מִפֶּתַח הָאֹהֶל וַיִּשְׁתַּחוּ אָרְצָה. (ג) וַיֹּאמַר אֲדנָי אִם נָא מָצָאתִי חֵן בְּעֵינֶיךָ אַל נָא תַעֲבֹר מֵעַל עַבְדֶּךָ. 

What is the relationship between Hashem's revelation and the guests' appearance?  Are the two connected or are they distinct events?  If the latter, why did Hashem appear to Avraham if the revelation was going to be abruptly interrupted before any substantive communication?

Three Men or Two Angels?

The guests who come to Avraham are referred to by different terms in the subsequent accounts of their activities.  In 18:2 above the guests are referred to as "אֲנָשִׁים" ("people").3  Yet, at the beginning of Chapter 19,4 when two of these same guests arrive in Sedom, they are described using a more ambiguous term "מַלְאָכִים" which sometimes denotes Heavenly angels:

EN/HEע/E
וַיָּבֹאוּ שְׁנֵי הַמַּלְאָכִים סְדֹמָה בָּעֶרֶב וְלוֹט יֹשֵׁב בְּשַׁעַר סְדֹם וַיַּרְא לוֹט וַיָּקָם לִקְרָאתָם וַיִּשְׁתַּחוּ אַפַּיִם אָרְצָה.

Are these "מַלְאָכִים" angels or humans?  If they are human messengers, is there any significance to the variation in the terms the Torah uses to describe them?  Conversely, if they are angels, why are they referred to as "אֲנָשִׁים" when they visit Avraham?  Additionally, either which way, why are there only two visitors in Chapter 19?  To where did the third member of the delegation disappear?

Angelic or Human Behavior?

The various actions of the guests are an additional factor which leads one to wonder about their identity.  On the one hand, the text shares that the guests were given water to wash their feet, that they ate,5 and that the people of Sedom wanted to sleep with them.  All of these activities are normally associated with humans, rather than with celestial beings.  On the other hand, the visitors appear to have supernatural knowledge and abilities.  They tell Avraham that Sarah will give birth, blind the people of Sedom, decide on their own to save the city of Tzoar, and perhaps even bring about the destruction of Sedom.6 

Ambiguous Appellations: Hashem or the Guests?

To add to the confusion, the chapters contain several verses where there is ambiguity regarding words usually used to denote Hashem.  It is unclear whether these verses refer to Hashem or the guests:

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