Excuse me. May I give you some suggestion too?
How about create offshoot development of eastern religion tree as
1. confucianism-->neoconfucianism and seperate taoism into other tree with very friendly relation with confucianism
neoconfucianism is the extreme development of confucianism in response to foreign religion (historically buddhism). It is much alike state doctrine that much more support the state power but in some aspect develop more on metaphysic and use more faith than ordinary confucianism. Neoconfucianism is responsible for state policy of China, Korea and Japan during 16th-19th century CE as it made China, Japan and Korea close border and turn to inward perfectionist of their culture but hurt civilization for the anti-innovation stance of the doctrine and hostility to foreign religion. For more information can find in wikipedia.
In term of the game neoconfucianism should use the same or have no contradict with confucianism believer. Start by great prophet when have foreign religion that shrine doesn't in your civilization border spread into your border. They will produce state culture like a mad(perfection of ancester culture) and increace growth rate but hurt you alot in global culture, research and a bit reduce wealth (neoconfucianists were socialist and sometimes act like economic blindness who did'nt understand how the wealth operated since they act as interest group). Allow you to build a defensive wonder which protect you from other civilization and babarian(historically is Ming's great wall which is the expansion of older great wall) and another economic boost wonder "Zheng He's Oversea Voyage" that can only be build under neoconfucian as a state religion but cannot use it effect until you switch state religion to other than neoconfucian. (Zheng He is half buddhist/islam eunuch and admiral in early Ming's court who went oversea exploration under emperor for economic and political greatness of China. Which later all official report of his vovage and his ships were order to be destroy by neoconfucianist beraucrats for inward perfection policy. But his legendry vovage inspire southern chinese to go and settle oversea to seek glory wealth and profit even it violate goverment's order but all of this oversea chinese proven to be useful to China later on after China open their border due to economic transaction, oversea chinese's investment on China's fatherland, technology and sometimes espoinge)
I would suggest that Taoism should allow enviromentalism civic when it is state religion.
2. I would suggest you let's buddhism can develop further into three sect, Thravada(represent as ordinary buddhism), Mahayana Buddhism and Tantric Buddhism (Vajrayana of tibet is one part of it.). With religion tree like this.
Buddhism-->Mahayana Buddhism-->Tantric Buddhism
all three buddhism can use each other the buildings and most of its wonders but different in game bonus (which should not much to balance the wonders effect below and should get production plenalty if possible) and have seperate believer since seperate ways of doctrine so it should cause a bit disadvantage for have different sect in the same civilization .
I agree with you in how to found buddhism and it bonus(but I want you to increace research bonus a bit and more spread rate than Hiduism). Once found buddhism it should allow you to build 2 wonder, Nalanda (first buddhist's university and the best known in medieval India for both religious and worldly subject. Later destroy by the turkish conqueror. For more information, visit
www.wikipedia.org ) which grant you research and great people boost can be expire later.(but not happiness since Thravada Buddhism originally monastaic and quite intellectual oriented.) And Temple of Tooth Relic (original in Sri Lanka) Which grant more happiness for Buddhist's temple can be expire( Represent the further development Thravada buddhism to more social oriented outside india. ).
Mahayana Buddism found by great prophet(historically, Nagarjuna) along with Nalanda University. Mahayana buddhism is more social orient and catch lower market sect as they are believe in saving all life and soul as their ideal. Their temple should produce more content citizen and spread fastest among all buddhism (they are once spread cover central asia before coming of Islam and fareast) and their bonus produce more coin and culture but less in beaker since they are less rational compare Thravada Buddhism. With Mahayana as state religion should allow you to build Buddhas of Bamiyan that boost economic and trade routes(corelated to silk road), Sholin Temple that automatically produce Sholin's monk (unit may count as warrior/scout/missionary) and allow to build warrior monk but expire later by technology (Sholin temple in china and warrior monk tradition in japan represent another side of idea of compassion that born in india. While india compassion end in pacifism, Fareastern Mahayana buddhism develop into use their on power to protect another even if it violated pacifism.) and Cults of Kuan Yin (project)(female bodhisattva of mercy of fareast tradition, the variation of originally male Avalogitesvara of india, which second widest worship in buddhism, second to buddha himself, and is widely known in fareast or any place that effect by chinese culture both classic and temporary) which add some happiness to all city with buddhism.
Tantric Buddhism found by Trantrism (project build by hinduism) but splited from Mahayana Buddhism. It is the buddhism that believe in instant knownledge, shortcut to enlightenment and supernatural power that in influence by tantric philosophy of india but still believe in concept of mass oriented saving of all life and soul as in Mahayana ideal. It should have bonus to support the state power in term of war and culture (since tibet once Dali Lama is the ruler both worldly and spiritual with temple as government center. With this they fight as aggressor against Butan and as defender against China) but reduce in coin and beaker since they less promotion on trade and least rational type of all buddhism. It allow to build wonders Potala Palace which reduces maintenance in nearby cities, generate gold for each tantric buddhism city and have all temple count as Broadcast tower and bunker but will not work unless your state religion is Tantric buddhism and Burobudur that add effect of temple and increace culture production and can be expire.
3. Should change tech tree of Hinduism to this.
Bhraminism-->Hinduism-->Sikhism( along with Islam)
-->Jainism
Bhraminism should allow you to build wonder Taxila (Learning center in ancient and classic india) no spread outside border.
Hinduism is found by have more than one religion shrine in border. Have higher spread rate than Bhraminism and better production bonus but use the same temple and shrine of Bhraminism. Should allow it to build Angkor wat and Tantrism (project)(a tradition and philosophy that inflence all aspect of india art, culture and religion)which increace spread rate of and hinduism, increace chance of Great artist, great prophet and great scientist and splited trantric buddhism from Mahayana buddhism.
Sikhism should be separate religion that will be found by have both hindu and Islam in your border and need great prophet. Should have warlike and state bonus since the history of struggle against odd of intorelant rival and born from idea to end conflict of hindus and muslims but not spread outside border.
Jainism should be separate religion that allow to use pacifism to the full potential( jainism is the one who develop pacifism in india) and doesn't spread to outside border.
4. Tech tree of islam should be
(from Eusebius's)--->Islam-->Sunni
-->Shia
Islam should start by great prophet with condition as you state but should give them a free shrine(Kabah Rock). Shia should become seperate religion sect since history of both intorelant of Sunni and Shia against each other but share the same main shrine (but shia will have other wonder that as their own shrine. While Sunni have quicker spread rate, Shia should have some battle bonus instead due to their violent struggle.
5. Catholism, Sunni, Shia should their own religion war unit since they have concept of holywar (such as Templer for catholic, Assasin for Shia, Ansar for Sunni etc.)
6. Howabout have othrodox christain too? as it should splited once someone build Papacy
7. How religious wonders can be use by any civilization that control is due to their state religion food chain and civic such as
the abrahamic group, the higher in food chain can be use wonders of the lower one but cannot use across food chain group such as Judaism cannot use woder of hellenism, all Christianity and all islam, islam can use wonders of all lower food chain include zoroasterianism due to their tolerant toward these group but Sunni cannot use Shia wonders due to their intolerant to each others
The Confucianism group, all first level religion that found in fareast can use each others include whole line of buddhism wonders but neo-confucianism can use only confucianism wonders.
The indic group, every religion in this group can use bhraminism wonders. Sikhism can use all hindu, bhramin and abrahamic line. Buddhism can use all wonders in their separate chain. Hinduism can use all wonders in indic food chain(no matter higher or lower in food chain) with additional of hellenism and mesoamericanism due to their extremely inclusive nature of their religion. Perhap hinduism should allow to build Hindutva project in modern age that allow you to use all religious wonders no matter what chains it reside.
Mesoamericanism can use all polytheism religion wonders such as hellenism, Bhraminism, Hinduism, Mahayana buddhism and Tantric buddhism due to their polytheistic nature.
Secularism cannot use other religious wonders except confucianism and neoconfucianism and secular wonders with little religious ties.