"He wants breakfast."
Translation:उसे नाश्ता चाहिए।
Do you mean उसे and वह?
उसे is the dative form of वह and roughly means 'to him/her/it'.
To see whether you have to use उसे or वह (when उसे/वह is used as a pronoun he/she/it not as 'that), replace the pronoun in the sentence with a noun like पीटर. If there is no postposition after पीटर in the new sentence, you need to use वह. If पीटर is followed by the postposition को, replace पीटर को with उसे.
Eg: पीटर गाता है (Peter sings ) -- वह गाता है (He sings)
पीटर को किताब दो (Give the book to Peter) -- उसे किताब दो (Give the book to him)
पीटर को मेरा गाना पसंद है (Peter likes my song, literally: To Peter, this song is liked) --उसे मेरा गाना पसंद है (He likes my song, literally: To him, my song is liked) (more natural way of saying)
पीटर मेरे गाने को पसंद करता है (Peter likes my song) -- वह मेरे गाने को पसंद करता है (He likes my song) (also correct way of saying but used less)
पीटर को नाश्ता चाहिए (Peter wants breakfast, literally: To Peter, breakfast is needed) -- उसे नाश्ता चाहिए (He wants breakfast, literally: To him, breakfast is needed)
पीटर नाश्ता चाहता है (Peter wants breakfast) -- वह नाश्ता चाहता है (He wants breakfast) (also correct way of saying)
उन्हें = 'to them' उसे = 'to him'/'to her'.
The latter refers to a single person while the former to multiple people. (Though उन्हें can also refer to a single person when you're being respectful/formal in which case the word referring to that person is treated as plural).
Above you have said वह नाश्ता चाहता है is correct. I have written exactly this and had it rejected. These questions only accept the oblique form. The direct alternatives need to be added and accepted. It seems that all the sentences referring to want in this section have this issue