Translation - French-English - Quand les voisins musulmans tuaient le mouton de...

Well I would say "courtyard" to be sure it's more accurate. But perhaps it's just the same thing.

We call le mouton de lait (little sheep) and not de l'Aït. But if l'Aït is the celebration that's correct.

(...) the entire court was enjoying (it's not "enjoying" but something like that... Lilian help!) of the celebration (...)

I think "benefit" is fine, they would take advantage of the feast.
Conditional (would benefit) is also right here.
However you are right, "celebration" would fit better

But "profitait" is the Past and in English is the Conditional Or not?

Yes, but sometimes, the conditional is not rendered as conditional. In English verb tenses are not that simple. That's why literal translations are not always correct
Believe me, here the conditional is fine

To be honest, I would not even be able to explain why I used conditional. It just sounded right.

Lilian, I have a question, why did you edited the translation, modifying the "Eid sheep" into "the sheep at Eid" ? It's a very particular sheep, that's why I wrote that... Explanation ? (God, days of university feel suddenly verrrry far ^^)

Hi LeFaune, most of the time what sounds right IS right .

I edited because "Eid" is not a 'kind of sheep', but the sheep which was sacrified at (the time of) Eid. Besides the definite article 'the' makes the particularity.
I hope I made myself understood

You're totally right. I read it with that explanation and that's perfect.

*bow*