Regarding first example sentence,
1) The guy being familiar with the city showed us around.
I would say that it's been used as an obsolute construction. The Wikipedia says:
In linguistics, an absolute construction is a grammatical construction standing apart from a normal or usual syntactical relation with other words or sentence elements. It can be a non-finite clause that is subordinate in form and modifies an entire sentence, an adjective or possessive pronoun standing alone without a modified substantive, or a transitive verb when its object is implied but not stated.
Your second example sentence is used as comparative, as its usage suggests considering everyone but mentioning only one guy who is familiar with the city (as Hot Licks mentions in the comments).
- The guy familiar with the city showed us around.