Religion Affinity, New Religion Mechanics, and Possible Religious Cultures

Good points and ideas. I'm offering ideas here and would encourage you to explain what you would do differently (I'm not 100% sure I got everything you were explaining ^^' )

1. Start with polytheism or shamanism as usual
2. Adopting your first tenet forms a "local religion"
3. A local religion is "upgraded" to "world religion" status when it gathers enough followers (and/or other conditions are met)
4. World religions have their tenets selected via a council of the faithful
5. Rejecting a decision of a council of the faithful can cause a schism and/or a Holy War
6. New tenets about how the religion is organized (how does the council of the faithful works? is there a central figure like a Pope? Is there a Holy land? A Holy See? A Sacred Temple? A Sacred City?). For example, a world religion with a Holy City could have the player controlling the Holy City make decisions on behalf of the council (with some exceptions requiring a full council vote, like when to declare a Holy War).
7. World religions have event and bonuses applied to all followers (the more followers of the religion you have, the greater the impact - this incentivize cooperation instead of systematically causing schisms every era)
8. Religions with competing interests/beliefs/demands will create "religious tensions" and lower stability, thus incentivizing uniformity for empire struggling to stay afloat. Inversely, "Religious unity" would grant stability bonuses. This would create a balancing act between collecting various religious bonuses and focusing on growing specific one(s).
9. Creating a Schism grants you with a local religions sharing the same tenets as the World religion you splintered from, with the contested tenet replaced (cause of the schism). Such religion can be upgraded to a World religion if enough people adopt it.
10. Local religions sharing the same tenets can trigger an event offering them to merge. If both councils of the faithful agree, the local religions are merged and may be elevated to World Religion status if the conditions are met. This can allow a schism to be mended. A reunified church would have many followers and thus greater bonuses, but individual players' control over it would be diluted in the bigger council of the faithful (which could be irrelevant if the religions uses a Pope instead).
11. "Religious proximity" metric would be useful, akin to the "Cultural proximity" indicating how tolerant another empire is towards yours. Religious affinity could influence such a metric like the Aesthete does for the Cultural proximity.
12. Changing state religion would cause a stability penalty. Entering a state of revolution due to a religion change would make it a civil holy war, with cost of changing religious civic/state religion lowered.
13. Council/Pope can sanction a player, which causes the "Religious proximity" to be (artificailly) lowered for that player for the follwoers of the religion and followers in the target's empire will cause instability (and potentially a civil holy war if the unrest is too severe). This can pressure a player to conform with the rest of the religion's adherents or to leave the council through a schism. Being sanctioned by the religious authority of your state religion would cause greater impact than a non-state religion.
14. Atheism would have the lowest possible "Religious proximity" with all religions and their followers always cause tensions/instability for empires with a state religion.
15. Secularism would not be affected by Atheism's instability, but is still susceptible to religious sanctions instabilities (all treated as a non-state religions).

[EDIT: Changed the format for a numbered list to ease discussion]

- Start with polytheism or shamanism as usual
- Adopting your first tenet forms a "local religion"

- A local religion is "upgraded" to "world religion" status when it gathers enough followers (and/or other conditions are met)

- World religions have their tenets selected via a council of the faithful
- Rejecting a decision of a council of the faithful can cause a schism and/or a Holy War

I will comment little by little so it would be easier to handle. I really like how you organized your topics. 

Well, yes. Every culture would eventually develop its local religion, probably after gathering a certain amount of faith, and this local religion would be basically what we already have as Shamanism and Polyteism. However, I think that every local religion could choose a tenet - or maybe more than one - and the tenets of the local religions are different from the ones of the world religions. This tenet of the local religion would be longlasting, regardless of the world religions present in the empire. This way, we could grant that even the peoples who follow the same world religion have some localized colour which is a result of a religious syncretism. 

As for how a world religion forms, I really like the idea of having a certain amount of followers and/or faith, but probably we should also research a technology and/or unlock a civic. Whatever would be the conditions to form a religion, once they are met, a prophet would appear and he/she would found a world religion. A world religion is a byproduct of its local religion and as so, the first tenet of a world religion should always be aligned with it. Let's say that the local religion tenet is a militaristic one, in order to create the new world religion, you must choose for you base tenet also a militaristic one. I'm considering the idea that when you found a religion, other than the base tenet, you could also choose other two, which could be of any kind. if that's the case, we could have a diffence between base tenets and additional tenets, being the base tenets the ones that grants more bonuses. (let's say, 15% more than it it was a mere additional tenet).

The player who founds a religion selects its core tenets, however, as the game progresses and the religion spreads out, there would be concils of the faithful and the new tenets of this religion would be voted by the players. The more folowers of this religion a player have, the more power he would have in those decisions. There would have a possibility of schisms during these concils of the faithful and it would be a result of a draw. So let's say we have 6 players in the concil. Two of them have the majority of the followers and they choose different tenets. If during the negotiations they do not agree with each other - I think that there should be a possibility for negotiating it - a schism could be the result. A faith that springs from a world religion would also be a world religion. Conversely, I also like the idea that a schism could emerge as a result of not accepting the result a Concil of the Faithful.

A player has also the ability to found more than one religion.

A side commentary:

I'm also considering the possibility that not all tenets are available to be selected during a Concil of the Faithful. Probably the pool of choices should be limited to the inclination of the empires that partake in it. Let's take Protestantism as an exemple. If you see the core tenets of the Catholic Church, especially during the medieval era, they were very non materialistic and even condemned certain monetary practices. But the tenets of Protestantism are much aligned with Capitalism. Maybe the pool of choices could be a result of certain aspects of the cultures that are thriving, in spite of the cultures affinities. This way, we could make the choices reflect how the peoples are developing during the game. If that's the case, the player who has more followers of that culture would delimitate more the possible tenets to be chosen, but the other ones also influentiates, proportionally to their number of followers.

I'll comment your other topics later.