Popularity of Buddhism among Mongol Tribes

It seems to me that Buddhism was really popular among the Mongols, East of the Chagatai Khanate. This made me wonder how and why Buddhism was so popular and not other religions like Islam, (Nestorian) Christianity or Hinduism? Although there answers such as "they are closer to the religious centre"... That may be true but that does not seem enough to me.

My questions are:
- Why was Buddhism so popular among Mongols within the border of the Yuan Dynasty?
- Could Islam, Christianity or Hinduism have a chance to replace Buddhism among the Mongolians?
- If yes, what is needed to achieve this?
- If yes, what are the consequences of the Mongols turning (1. Islamic, 2. Christian, 3. Hindu)?
- Would it also affect the Manchu's, influencing them to turn Islamic, Christian or Hindu?
- If the Mongols (and Manchu) turn Islamic, will they be absorbed by the local Hui Muslims and Uyghurs?
- Did Buddhism halt the aggressive expansionism of the Mongols post-Yuan dynasty? Or was it the division among the Mongols rather than their believes?
 
Buddhism has been present in Northern Tatary since the days of the Uyghur Khaganate, empires like the Khitan Liao and the Jurchen Jin turned into Buddhism as seen as "traditional" with other religions like Christinaty and Islam being far off and thus less relevant (mind you that Islam did take off on the western steppes closer to the Islamic powers, there converting to Islam had real benefits).
The Yuan itself was a main drive towards the eastern Mongols convertion into Buddhism, with Kublai was always being pro-Buddhism, his wetnurse being a Buddhism Tangut that he was greatly fond of and as one great sinophile he was immediately attracted to Chinese buddhism, after the conquest of China he invited Tibetan lamas (why Tibetan Buddhism instead of traditional Chinese rites is unknown to me) to his court in Khanbaliq and with the Yuan dynasty being primarily a Sino-Tibetan centric polity Sino-Tibetan cultural influences (esp. Buddhism) became the main influencers of Mongol culture.
After the fall of the Yuan my knowledge gets hazier, but the Northern Yuan tribes seemed to have direct influence in Tibet (see the Khooshud Khanate) instead of
 
After the conquest of China he invited Tibetan lamas (why Tibetan Buddhism instead of traditional Chinese rites is unknown to me)

I'm speculating that it was from a desire to avoid local politics around Buddhism in China, since it was often anti-Imperial. Esoteric Buddhism had a lot of presence in China's various mass rebellions too.

After the fall of the Yuan my knowledge gets hazier, but the Northern Yuan tribes seemed to have direct influence in Tibet (see the Khooshud Khanate) instead of

Yes, there was a direct link to Tibet through conquest or occupation by both the Mongols and the Oirats. And opposition to China, as usual.
 
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