"Are we men or lawyers?"
Translation:An fir nó dlíodóirí muid?
"An" by itself is the question form of the copula "is." It is used whenever you form a question with "is" like "an maith leat bainne?" "An bhfuil" is the question particle "an" plus "bí" in the dependent form. You use "an bhfuil" whenever you form a question with "bí" like "an bhfuil tú ag léamh?"
We. It is an older form, and much used in Munster dialect. Muid is more widely used elsewhere, but there is overlap. Best known example of sinn is in the name of the political party, Sinn Féin, or in the national anthem, Amhrán na Bhfiann (Song of the Fianna popularly known as The Soldiers' Song), which starts with the stressed form Sinne Fianna Fáil, atá faoi gheall ag Éirinn (loosely: Soldiers are we, whose lives are pledged to Ireland.)
All of your questions are about copular statements. In general, word order in Irish is fairly straightforward - it seems complicated to people who are so inured to English convolutions that they get confused when things are straightforward.
(That's not to imply that the copula is straightforward, but part of the reason that we find hard is because it doesn't work the way English does. But that shouldn't be your yardstick).
I don't find the VSO order particularly difficult, and that is shared by all Celtic languages. It may be the Irish copula alone that confuses me. It may also be, as you appear to aver, that English speakers are simply particularly thick headed. I am a native speaker of English, but I do have some exposure to other languages, so I wouldn't have thought I was particularly limited to an anglophonic point of view. Word order has never been a particular problem for me in any of the other languages I have studied, except for Irish (Klingon as well, if that counts).
I'm a bit confused. You asked a couple of questions on different threads about how to use pronouns in copular sentences (this one and Cé hiad na hoibrithe?) so I pointed you to a thread about the copula, and you say that you wouldn't have thought to look there because you were only asking about word order, but then you say that you don't have any problem with VSO? That suggests that you could pick out the verb in An fir nó dlíodóirí muid? and Cé hiad na hoibrithe? and therefore knew that you were dealing with the copula (there isn't any other verb in either of those exercises), and therefore looking for insight to where to place the pronoun in these copular sentences in a thread entitled "Eureka Moments with the Irish Copula: A Crib Sheet" doesn't seem much of a stretch. If you couldn't pick out the verb, then I don't understand why the position of the pronoun would be your first point of confusion.
You use the copula when you use a noun or pronoun ("we") to identify or categorize a noun or pronoun ("men" or "lawyers"). So you say Is fear mé, not "tá mé fear". Therefore, you don't use the interrogative form of tá (an bhfuil?) when you turn this into a question, you use the interrogative form of the copula (an?).
This is the case even in Ulster Irish.