indirect object
An indirect object is the receiver of the direct object. The assembled children are the ones who are receiving the information the meteorologist is telling. The subject of the sentence is who or what the sentence is about. The meteorologist is the subject of this sentence. He is doing the action. A predicate nominative renames the subject. It follows a linking verb. There is no linking verb in the sentence so predicate nominative is not an option. An appositive is a noun phrase that renames or describes the noun next to it. For example Sarah, my sister, is late. My sister is an appositive; it renames Sarah as my sister.
2, 4, 3, 1 that is the answer going down the list
This is a participle. It cannot be a gerund, because gerunds have a nominal or adjectival meaning (for example, Swimming is fun - swimming would be a gerund). The -ing form itself is not a 'verb phrase', but 'sneezing uncontrollably' is. So if we are looking only at 'sneezing', the answer is 'participle'.
To cast down your bucket where you are means that you don't need to travel far in order to find what you are looking for - there are many valuable resources exactly where you are.
What Washington is trying to say here is that he wants both black and white people to work together and rebuild the South in order to make it prosperous and forget about their differences.
