The adverb phrase that describes "will see" is "after school". This is an adverb phrase that describes the time: when does the action of the verb occur.
An adverb phrase is any phrase that acts as an adverb - that is, it describes or modifies a verb (most often), another adverb, or an adjective.
In this case, we can easily see that this is an adverb phrase, by replacing it with a common adverb, for example - later.
The dialogue develops the characters because it shows that A. Aunt Mary is afraid of fire; and D. Kaydee is a calm person.
Aunt Mary acts nervously around his niece trying to star the stove and is afraid that she is going to set the house on fire, but Kaydee remains calm and explains the situation without being rude.
We are eating dinner now
I hope this helped :)