1. It is my brother’s guitar.
Great! It means that the person possess a guitar.
Wrong! It’s not the verb to be, after's there is a noun. It expresses who the owner is.
2. My father’s 63 years old.
Wrong! It’s not a possessive case because the age is not an object that can be possessed, it’s a state.
Excellent! Here the verb to be refers to the father’s age.
3. They’re the children’s toys
Totally right! The's means that those toys belong to the children.
Wrong! It’s not the verb to be. After's there is always a noun.
4. My aunt’s name is Amanda.
Sure! The's expresses that her name is Amanda.
Wrong! It’s not the verb to be since the meaning would be illogical.
5. My friend’s Canadian
Wrong! It cannot be the possessive case since in this sentence Canadian is an adjective not a noun.
Right! The verb to be is used to say his nationality: My friend is Canadian.
6. My sister’s a nurse.
Wrong! It cannot be the possessive case since it does not express a belonging.
Excellent!The verb to be is used to express an occupation: My sister is a nurse.