There really isn't much lore anywhere in game about the religious traditions or rites of Eorzean gods, except maybe Ishgard, and even then all we get is that they have the silliest method to discover heretics. Everything else is vague and all we have is that there's reverence to those who died (seen in the graveyard north of Drybone: people make offerings to the dead) and that you can pray to the gods. Do they have specific prayers? Specific offerings to them? How is their priesthood? What we can infer is that some priests seem to be of the catholic-ish variety (again, from those in the church north of Drybone), but then I have no idea who they are supposed to be priests of. Nald'thal, maybe?
Let's go back to the relationships between gods. I can't find why you think Nymeia is Rhalgr's wife. She is his master, but Halone and Byregot aren't childrens of her. At least there's nothing in lore suggesting that. Though I guess you could imply that Rhalgr had to be with a goddess in order to have those two.
However, since the gods seem to be more metaphysical than physical (unlike, say, the Primals, who continuously manifest in the world with a body), any relationships between them must be by definition metaphorical.
So, let's see. We have Fate (Nymeia) and Time (Althyk) being brothers. Time is the father of the Sun/Inquiry (Azeyma) and the Moon/Love (Menphina). The Moon is married with the Wandering (Oschon), who is brother with Trade/Death (Nald'thal, who are actually Nald and Thal, two aspects of the same god, often refered to as twins).
Then we have that the Sun/Inquiry (Azeyma) and Knowledge (Thaliak) is mother of Fertility (Nophica) and Navigation (Llymlaen).
To finish, we have that Destruction (Rhalgr) is father of War (Halone) and Craftmanship (Byregot), with the later being also pupil of Knowledge (Thaliak).
With all those relationships, and with my stomach empty, I can deduct the following:
-Nymeia, Althyk, Thaliak and Rhalgr are the main gods, as they are the only ones that weren't created by divine marriage.
I should probably spend more time thinking on this subject, but anything that sprouts from there will be just speculation. There's not much in-game (that I have seen, anyway) to infer, induct or deduct about the religion of the place besides "Yeah, gods. They are a thing and you can pray to them!"
Let's go back to the relationships between gods. I can't find why you think Nymeia is Rhalgr's wife. She is his master, but Halone and Byregot aren't childrens of her. At least there's nothing in lore suggesting that. Though I guess you could imply that Rhalgr had to be with a goddess in order to have those two.
However, since the gods seem to be more metaphysical than physical (unlike, say, the Primals, who continuously manifest in the world with a body), any relationships between them must be by definition metaphorical.
So, let's see. We have Fate (Nymeia) and Time (Althyk) being brothers. Time is the father of the Sun/Inquiry (Azeyma) and the Moon/Love (Menphina). The Moon is married with the Wandering (Oschon), who is brother with Trade/Death (Nald'thal, who are actually Nald and Thal, two aspects of the same god, often refered to as twins).
Then we have that the Sun/Inquiry (Azeyma) and Knowledge (Thaliak) is mother of Fertility (Nophica) and Navigation (Llymlaen).
To finish, we have that Destruction (Rhalgr) is father of War (Halone) and Craftmanship (Byregot), with the later being also pupil of Knowledge (Thaliak).
With all those relationships, and with my stomach empty, I can deduct the following:
-Nymeia, Althyk, Thaliak and Rhalgr are the main gods, as they are the only ones that weren't created by divine marriage.
I should probably spend more time thinking on this subject, but anything that sprouts from there will be just speculation. There's not much in-game (that I have seen, anyway) to infer, induct or deduct about the religion of the place besides "Yeah, gods. They are a thing and you can pray to them!"