Hello Starwave, welcome to UsingEnglish!
I would say that your analysis of the meaning of 1 and 3 is correct. However, it seems to me that the "standing" clause in #1 could be interpreted as a reduced adverbial ("I, while I was...") equally with #3.
#2 is ambiguous: we do not know who was standing there, the subject or the girl.
Adverbial phrases can indeed end sentences, as in your "breakfast" example.
In the "Buster" example, I would take "deep" as a post-positional adjective: there is no need to treat it as a reduction.
To turn to your last and more general question: I am not entirely sure it is necessary to attempt to distinguish between adverbial and adjectival phrases, in examples of this kind. For instance, although it is possible to interpret the "standing" clause in #3 as a reduced adverbial, the clause itself has an adjectival force: it tells us something about "I" which does not necessarily coincide with the duration of the "seeing".
In other words, perhaps a reduced adverbial clause can become (in effect) an adjectival clause.