No problems with what you are planning, as for the questions, religion spreads like it does in the OTL but slower especially in land as coastal areas become focal points as well as river valleys. Islam and Christianity spread much more slowly, in fact horses played such a role in the spread of both, especially Islam that many places will not see either for centuries if at all. There is a good chance that Muslims do not spread North into Byzantine/Rome or Persia territory without horses. Islam may become a maritime religion that spreads along the coast of the Indian Ocean and South Atlantic. Zororastrianism survives and Southeast Asia becomes Hindu/Buddhist mix with local animist traditions thrown in. Islam is a traders faith.
Christianity reaches Scandinavia from the East instead of the West due to trade going from Byzantium/Rome. The British isles wait till 1000 CE or later until Christians come and again its through traders.
Granted Islam might be butterflied away due to all of this as well and Arabia gets split between the Persia and Rome/Byzantium. I think we will see a Persia-India conflict at least eventually.
As for the Americas it might be delayed centuries by all of this.
Thanks for your input,
@wtw !
As others have pointed out, I think it is safe to assume that there won`t be any Christianity or Islam in this world, and neither will there be Buddhism.
Some of what is under the umbrella of Hinduism might exist and become more prominent, though, while other stuff certainly won`t.
Since I take a minimal butterfly approach, too, I would think that at least some type of Israelites would emerge, since their revolt / exodus occurred early enough for no-horse-effects to be still limited in Northern Africa. OK, Moses as a person may be butterflied, or he might just be a guy with a different name, living under a different pharaoh, but the conflicts and tensions between civilizations like the Egyptian and the herding periphery, and the racism with which Egyptian Kingdoms treat the Habiru / Apiru living in their realm might not go away. So some sort of liberation movement might occur nonetheless, an alt-Moses.
But such an alt-Judaism won`t be anything like OTL´s Judaism: no horses mean no Neo-Assyrian Empire = no Babylonian exile, so they can`t come into contact with Zoroastrian ideas which tipped the balance in favour of monotheism among the Israelites. BTW, no horses = no Iranians in Iran = no Zoroaster, either. Also, the Canaan they might invade (if they choose to go in that direction at all) would look different since this is a world without a Hittite Empire, without Hyksos, and maybe with a completely different end to the Bronze Age instead of OTL´s collapse.
Christianity, on the other hand, requires Hellenism and the Roman Empire, neither of which will exist. (Which of course also means no Byzantium. Not even a Persia, btw.) Islam requires Christianity and a lot more which won`t exist. And Buddhism requires Vedic religion, which won`t exist, either, without an Indo-Aryan takeover of Northern India.
So, the religions I´m left with are those of Egypt and the Fertile Crescent, of the Bantu and other indigenous African groups, the Australian and Oceanian aborigines, and of course of the pre-Columbian Americas. Also, some hints from Dravidian and Chinese folk religion.
But I suppose this won`t have to be it. There will be new developments from the 2nd millennium BCE onwards in this timeline, too. Alt-India may be a good place for that, or some other land on the periphery of the Middle Eastern civilizations. I just don`t have an idea what such a founder of a very different religion might preach...