"from the farmer" is a prepositional phrase. It is formed from the preposition, "from" and the noun phrase, "the farmer".
Prepositional phrase
A phrase is never a part of speech, only a word.
Noun
The phrase "in addition" is a prepositional phrase in which "in" is the preposition and "addition" is its object. This phrase, as a phrase, is not a part of speech, although it may function as one, probably an adjective or adverb.
A prepositional phrase.
On the mountain top is a preposition phrase, not a part of speech.
That I am is a phrase, the individual words in the phrase are parts of speech. That -- demonstrative, determiner I -- pronoun am -- be verb
"That" is a pronoun, while "I" is a pronoun and "am" is a verb.
adverb phrase
verb
A prepositional phrase.
A prepositional phrase.