So many ways to say 'want''... I hadn't seen this one before, given all the other possible ways (uaidh, teastíonn....uaidh, tá sé ag iarraidh,..), is this one in use? Or does it have a shade of meaning different from the other (more common?) ones?
Yes, it’s used — a literal translation of Tá fonn air would be “A desire is on him”.
How would this differ from 'is mian leis...'? Would it be that 'Tá fonn air dul abhaile' - He desires to go home. 'Is mian leis dul abhaile' - His desire is to go home?
"he would like to go home" was my contribution but afách bhí sé mícheart
He has a yearning to go home - marked incorrect.... yearning / desire / want ......on him... Very little obvious difference to me in this context anyway.
Duolingo isn't testing you in your comprehension of Irish, or your English vocabulary, it's teaching you a basic but functional vocabulary in Irish. In that basic vocabulary, fonn is taught as desire, and rendered as "want" in this sentence, because it's a better idiomatic sentence in English.
The contributors didn't go through a thesaurus and add every possible translation to every exercise. You can request that they add alternative translations, but really, is it worth their or your effort in this case?
I think also that the meaning of "want" in English (at least in the US) has drifted from the meaning "need" and "lack of" over toward the idea of "desire". We read in literature but rarely say "they are in want of x" when we can more commonly say "they are in need of x". The sentence "Tá ríomhaire uaim" expresses that the computer is "wanted" not because of desire so much as because it is "needed" (for not being here, i.e. "at me" or "have"). Tá fonn orm ríomhaire níos fearr ach níl ríomhaire uaim. "I desire a better computer but I don't need a computer" is more understandable than "I want a better computer but I don't want a computer." Tá súil agam go raibh sé cabhrach.
"Tá fonn air" is probably very close to the French "il a envie de". In this instance, the English language does not allow for subtlety.