The above exchange shows how to make a polite request for an action and how to consent to the request. おV(ます)します is a humble polite expression which is used when the speaker offers to do something for the hearer, who is "superior" to the speaker.
The verb いただく is the potential form in negative question format, which expresses a request: Vていただけませんか. Note that it is NOT "Vていただきませんか". The Vてさしあげます pattern can be used when describing to someone else what the speaker does for one's "superior", but the おV(ます)します pattern should be used when speaking to the "superior" for whom one offers to do something.