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The prepositional phrase is "under the couch".
Under the bush, ''under'' is the preposition.
There is no possessive noun unless you change the phrase to read, 'the children's telephone'. In this example the possessive noun is children's.
The gerund phrase in this sentence is "children singing."
"The children were running to the bus stop." The verb phrase is "were running."
No it's a phrase. Nouns are a person, place, thing, or idea. A phrase has more than one word each of which is its own part of speech. Your phrase is "Two children look in" Two is an adjective. Children is a noun. Look is a verb. In is a preposition.
"children singing" is the gerund phrase in this sentence. It serves as the object of the preposition "of".
In this sentence, "were running" is the verb phrase, in the past continuous tense.
children singing
I'm not sure I understand your question. What phrase are you asking about, "children for school?" If that is what you mean, it could be correct depending on how it is used in the sentence. For example, a sentence such as "We must prepare the children for school." would be correct. If you make your question a bit clearer I could help more.
The gerund phrase in the sentence is "children singing." It functions as the subject complement that describes the favorite sound.
Children singing