So... another way of saying "where" is "cá bhfuil", OK. Would it be incorrect to use "cén áit" or "cá haít" in this sentence instead of "cá bhfuil"?
Oh, wait, I think I get it now! "Cá bhfuil" includes the verb "bí", so that's why it's used in this sentence, which literally means "Where is it that they ARE in their living?. Whereas "cén áit" or "cá háit" would be used for questions with other verbs, adding an "a" before the verbs (for example, "Cén áit a itheann tú?", meaning "Where do you eat", right?).
Or, maybe, could "cén áit"/"cá háit" also be used with the verb "bí", adding an "a" ("Cén áit a bhfuil siad ina gcónai?")?
Are any of my conclusions correct? Sorry for the rambling... I find Irish to be so confusing and complex... but I'm lovin' it thanks to Duolingo. :)
Irish has two relative clauses - a direct and an indirect.
The difference doesn't exist for most verbs (except initial mutation), but there are some that have a dependent form (form used with another particle an, for example, or ní) that the indrect uses. That's why it's cá bhfuil (cá requires indirect, which eclipses and uses dependent form which is fuil)
The main use of "cónaí" seems here to be related to the idiomatic expressions "living in/at" or "always", which usually would be lenited or eclipsed.
Cá bhfuil mé i mo chónaí? = Where am I living?
Cá bhfuil tú i do chónaí? = Where are you living?
Cá bhfuil sé ina chónaí? = Where is he living?
Cá bhfuil sí ina cónaí? = Where is she living?
Cá bhfuil muid inár gcónaí? = Where are we living?
Cá bhfuil sibh in bhur gcónaí? = Where are you living?
Cá bhfuil siad ina gcónaí? = Where are they living?
"ina = in his", "ina = in her" and "ina = in their" being distinguished by lenition / eclipsis on the following noun.
"i gcónaí" is a fixed phrase meaning "always".
EDIT: Nobody has corrected, so it is approximately right. Then question is of course, isn't there anything superfluos in those sentences. You'd think it couldn't be me in your living, so the "mé", "tú", "muid" and "bhur" should be totally needless?
I think, like me, you misheard the sentence. It's Cá bhfuil SIAD ina gconaí? I thought it was, 'Cá bhfuil SÍ . . . ' Therefore conaí is eclipsed whereas it wouldn't be with SÍ.
The basic rule is this: Mo (My), Do (Your sl. ), and A (His) - all aspirate consonants. A (Her) puts H before vowels. Ár (Our), Bhur (Your pl.), and A (Their) - all eclipse consonants and put N before vowels.