A verb phrase is the verb and its dependents (objects, complements, and other modifiers), but not the subject or its dependents.
The verb phrase in the sentence is "heard that our school is getting a new mascot".
The subject is the pronoun "You".
Note: "that our school is getting a new mascot" is a relative clause functioning as the direct object of the verb 'heard'.
(A+) the sentence is (or should be) "Has my brother arrived yet?" the verb phrase is "has arrived"
No. Why? And why would you ask this in the internet? ....
The verb phrase in the sentence "That dog will eat everything you set in front of it" is will eat.
Intransitive Verb.
"Could have moved" is the verb phrase, but the reflexive pronoun (ourselves) doesn't agree with its antecedent (you).
You could never have moved that tree yourself (yourselves if you is plural).
OR
We could never have moved that tree ourselves.
The verb phrase is will be.
I'm assuming you're asking which word in your sentence was a verb so it's show.
Improved:
The verb phrase is "could show".
intransitive
In the sentence, "he has always thought about his future" the verb phrase is "has always thought".
In the sentence "Shawn tells long crazy jokes" the verb "tells" is an action verb.
In the sentence, "Susan appeared confident about the debate." Appeared is a linking verb, it connects the subject "Susan with the rest if the sentence, it lets you know that she is confident.