"Me" is always appropriately used as the object of a sentence, while it is used in this sentence as the subject. The first person subjective pronoun "I" must be used instead. "You and I have" is the only answer choice that does this and uses the appropriate verb form "have."

The use of the pronoun "him" in the subject of the sentence is incorrect, as "him" should only be used as the object of the sentence. The proper third person male pronoun for the subject of the sentence is "he," making "He and I are going" the correct answer choice.

The use of the pronoun "him" is incorrect in the sentence, as it used as the subject, but can only be used as the object of the sentence. The pronoun needs to be changed to "he," but otherwise the sentence is absolutely correct. Therefore, the correct answer choice is "She and he have been."

The use of the pronoun "me" is incorrect, as it used as the subject of the sentence, but is only correctly used as an object. The form needs to be change to "I." The only choice which does this and is grammatically correct is "The boys and I are going."

The use of the pronouns "me" and "him" are both objective pronouns, but are used here as the subject of the sentence. They both need to be changed to the appropriate subjective forms "He" and "I;" therefore, the correct answer choice is "He and I have always."

The use of the pronoun "him," which should only be used as a sentence's object, is incorrect as a subject of the sentence. Thus, "him" needs to be changed to the third person subjective pronoun, "he;" therefore, "She and he were going to the dance after they had dinner," is the correct answer choice, as there are no other issues in the sentence.

The use of "I" in the object of the sentence is an absolutely incorrect usage, and needs to be fixed. The appropriate pronoun in the objective space is "me." As this is the only change that should be made to the sentence, the correct answer choice is "by both you and me."

The use of "she" in the sentence is incorrect, as "she" is a subjective pronoun and should only be used as the subject of the sentence. The pronoun should be changed to match "him," as an objective pronoun; therefore, the correct answer choice is "for both him and her."

The use of the pronouns "me" and "him" is incorrect, as both are in their objective forms, but are used as the subjects. Both pronouns need to be changed to their appropriate subjective forms. "He and I will always be" is the only answer choice that uses the correct pronoun forms.

The use of "I" as the object of the sentence is incorrect. There are no other issues in the sentence, so the only thing that needs to be done is to change "I" to the objective pronoun "me"; therefore, the correct answer choice is "The strongest supporter of the cause has been me."