Explanation: Irony is, by definition, the usage of language with a meaning opposite to what is expected. In this case, the adjective "prompt," normally attributed to someone who arrives early, modified by the adverb "unusually" before it sets the expectation of the doctor being overly punctual. When we learn that unusual promptness equates, for this person, to being half an hour late, we get the humorous emphasis that the speaker wanted to attribute to the doctor's <em>lack</em> of punctuality.
In this sentence, the word rapport means connection. If you have a good connection with your audience, then they can track with you and give positive feedback