1. Noun or noun phrase - yes: 'I ate a (big ham) sandwich.'
2. Pronoun - yes: 'I erased him.'
3. Prepositional phrase - no, not really: in 'I looked at his girlfriend', '(his) girlfriend' is considered the direct object, with the particular verb requiring the preposition (a phrasal verb). A real prepositional phase is better considered a verb complement: 'I stood on
Easy: finite clause has a finite verb (that is, with tense) and a non-finite clause has a non-finite verb ('-ing' and '-ed' forms without the main verb, or infinitives).