Lets go through your concerns. Firstly lets point out the invalid points of reference you made.
The Church has a conception of salvation, and is extremely concerned about achieving it for all.
The Church teaches of the existence of a soul, similar to that of the Abrahamic tradition.
The Church has a very active concern in converting all of its neighbours.
Also, you referred to the Grandpatriarch as a Pontiff.
Excepting the reference to the Grandpatriarch as a Pontiff, which I simply did not make, These concepts were part of the concept of the Church of Iralliam before I joined. Indeed if you read back, you find that the name Iralliam itself refers to a paradisiac heaven which was established at the foundation of the religion, while the religious brief on the front page clearly states that Iralliam has an evangelical impulse.
As to the remaining summations of yours
The Church uses an otherwise-dead liturgical language.
The Grandpatriarch is elected by a Clerical College of other archpriests of the Church.
The Grandpatriarch is the 'Vicar of our Lord on Earth'.
The Church is described as being universal in nature.
The Church has a taste for fresco art.
The Church propose the existence of natural law.
The Church possesses canon law.
I will go through these one by one.
1: Iralliam is an ancient religion, an ancient language as such seemed appropriate. Just as Buddhists use pali, and Buddhists and Hindu's use Sanskrit, Zoroastrians use their Avestan, Muslims use their Arabic and Catholics use their Latin. Heck even the amish use an archaic dialect of german. A sacred language is a near universal characteristic in most organised religions, and was far more common than using the vernacular until modern times and its trend to reject the traditional (separation of the sacred of the profane being intrinsic to religion in general)
2: The means of election of a Grandpatriarch was non-existent previously, so I decided to go with something somewhat familiar. Considering the Church uses patriarchates very much like greek orthodoxy (which is incidentally why I decided to use greek sounding terms when describing architecture and didn't decide to go creating new moti or liealb terms for the same. Why not call an aedicule an aedicule when that is precisely what is being described and when the whole architectural point is peripheral to the religion anyway), I decided a group of exalted priests in the Holy City was a reasonable enough means of election. Particularly considering we only have four other patriarchs all very distant from Opios, no well ingrained monastic practice, and no bishop analogues. There is likewise no actual detail as to the clerical structure (from what das told me, one does exist but has not been defined) save that it seemingly is not hereditary.
3: The use of the term "vicar of the lord on earth" is actually a reflection of his former near absolute authority on matters religious. In words that were not mine, once his word was law at least on matters religious. Such authority quite reasonably would be established by virtue of an association with the deity involved. Indeed in the absence of such a religious association I doubt Iralliam would of stayed as a unified religion, as compared to splitting on national lines like Eastern Orthodoxy did IRL, or into a multiplicity of sects.
4: Any religion worth its salt considers its teachings universal. That applies for Christianity, Islam, Buddhism and others alike. I'm not going to make Iralliam an exception, particularly when historically it has already been established previously that the prophets words are considered infallible, and when the Church has had heresies that it has clearly condemned historically (both things which presume a sense that the Church's teachings are universal within Iralliam).
5: If you associate fresco with Catholicism, be my guest. Its a false association (Catholics use all known means of architectural adornment) and since I happen to like religious wall painting through that medium I'll continue to use the term where appropriate to describe wall art to give the churches of Iralliam a bit more colour and life to them.
6: Natural law is indeed a Catholic concept. I decided to introduce it because I'm familiar with it and because from my background searches Iralliam seemed to be a more rationalist religion than say Machaianism and Indugahor, and somewhat wary of mysticism. In the absence of an overarching mysticism I thought it reasonable that some sort of natural law approach would evolve in Iralliamite exegesis, since in the absence of a pure mystic religion, or a clearly established prophetic law written in a large book in the style of the Torah, that sort of development seemed, well, natural.
7: Canon law as a term is Christian (I used it rather than creating some random term a priori, again Im not big on creating random terms that have no meaning divorced from this NES when a suitable term exists already to describe what Im trying to get across), religious law however is common to most faiths. The eastern religions have the concept (apparently in Theravada it is frowned upon to sleep on a large comfortable bed) as obviously do Zoroastrianism, islam, Judaism and others.
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Now moving on from the refutations. Firstly I understand you have your own position on religious matters as they apply in Helsia. Secondly, I understand you may have had your own previous interpretation on what Iralliam was before I joined, as sort of shows in your statements regarding the prophet (who says anything I said is contradictory to love, duty, forgiveness and loyalty, although acceptance of the evil of the dark God Istria obviously is anathema to Iralliam. That's part and parcel of a dualistic religion and again its something that pre-existed my involvement here). However since I run the Church as it stands, its not your place to determine its practice. Rather its your job to manage your nation, and deal with any issues that pertain to it as you see fit. I'm sure I would love to help you create a unique Helsia, one that is truly native to the setting of N3S and possessed of a unique nature all of its own, but I understand that its not my place to direct how you manage your own affairs.
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Now as to my vision of Iralliam. As I have said I fully intend on maintaining continuity with everything that has preceded my involvement. I have not, and will not, change anything that has been established about Iralliam (its agrarianist, dualistic nature is here to stay), nor will I make it some pale copy of Catholicism (indeed if we must use analogies, I see in terms much closer to a fusion of Eastern Orthodoxy, Zoroastrianism, and certain aspects of Hinduism and Shingon Buddhism than in terms of Catholicism). At the same time however I am not going to shy away from establishing organisational concepts that occur in religions in the real world within Iralliam, where they are appropriate and rational to the circumstance the Church finds itself in, just because you or anyone else has some aesthetic aversion to it. Nor will I avoid terminology associated with religions in real life in favour of creating new words that to my mind do not fit in with the naming schema already established (wheres your protest at the term Patriarch? that's a Greek term for you). You may not like the direction I am bringing Iralliam (much more emphasis on its evangelical component, and a move towards restoring the formerly absolute Grand Patriarchal authority that existed over matters religious) or the aspects that are similar to certain faiths in the real world, but with regards to the latters its erroneous to lay the blame entirely on me (the inquisition analogue (the order of faith), the patriarchal system, and its core doctrine for example did not originate with me), and with regards to the former its very much not my problem.
EDIT: Oh and if you think I intend to play Iralliam like the papacy in CI, than you are very much mistaken. The papacy in CI has political concerns at the forefront of its mind, whereas in this game the internal dynamic of the Church, and the spreading of the religion are the main priorities. Oh and CI is not my sole NESing experience, I have played in some other NES's that are no longer extant incidentally as normal nation-states. Thing is I only tend to play a few games at a time for my own sanity, and so I can put more into each individual game. So I am rarely in more than two games at once.