Answer:
1. The underlined phrase "The character and conduct of the nation" is a noun phrase, it is used as the subject of the sentence.
2. The underlined phrase "Abolitionists" is a noun phrase, it is used as the subject of the sentence.
3. The underlined phrase "Life, liberty, and the pursuit of happiness" is a noun phrase, it is used as the object of the sentence.
4. The underlined phrase "the rights of slave owners" is a noun phrase, it is used as the object of the preposition "of".
5. The underlined phrase "the wrongfulness of slavery" is a noun phrase, it is used as the object of the preposition "of".