The religion of Genghis Khan, Tengrism, was the religion of Mongols and Turks many of which still practice the faith.

Tengrism is not a single faith but rather an umbrella term of similar faiths with share traditions and Pantheons.

They believe in a 3 world cosmology of Upper world ( where the white spirits are from), the lower world ( where the black spirits are from) and middle where humans live and the spirits all mix. Above them all the eternal Blue sky the God Tengri or Tanrı

İt's important to not take this in a Abrahamic framework as the black spirits are not Evil demons and are not necessarily evil but aid in the more morally "grey" aspect of Human interaction such as Warfare or combat.

Where as the white spirits was more for Lay life and communication with the heavens.

The goal of Tengrism was the balance the two within yourself, not to be too barabric and warlike to the point that you ignore your family and your tribe but not too pacifistic that you allow other nations and tribes to dominate over you and subjugate your people. This idea of Balance runs throughout Tengri inscriptions. For example the famous Orkhon or Ötüken inscriptions focus on both warfare and conquest aswell as the peaceful aspect of tribal nomadic life , which seems strange for a historical documents but makes sence once you understand the outlook of the people regarding this balance

https://archive.org/details/Ross1930BSOASOrkhon/page/868/mode/1up

Here is the full English translation of the inscriptions if you are interested.

To come back to your question specifically. İt's clear that Tengrism was not completely against killing or warfare and possibly even Justifies it as a natural part of achieving this balance. This is also why Genghis khan is also famous for his home reforms and taking care of the people who did not go off to war and the widow's of fallen soldiers.

Edit: with regards to the religious tolerance this is clear from the famous quote from Möngke khan, 4th khagan of the Mongol empire, where he says " As Tengri as given us 5 fingers, he has also given us many ways to approach him". what is evident from this is that Tengriists saw other religions as worshiping the same God but in different ways and as such would not of had any issue with them. This quote was a part of a letter sent westwards towards the pope and the then king of France.

Absolutely. The myths of Temujin's (Genghis Khan's birth name) birth and ancesty are infused with divine events and is said to have occurred at the most sacred site of Mongolia, the God Mountain Burkhan Khaldun. He would return to Burkhan Khaldun throughout his life to engage in shamanic ritual on the mountaintop to receive wisdom and guidance from Tengri. He would ascend the mountain alone and unarmed and stay for days while seeking guidance from Tengri. The first story of his encounters with Tengri happened at age 12 and continued throughout his life.

As Temujin, and later as Genghis Khan, he would return to Burkhan Khaldun before launching any major military campaign, while his envoy would remain at the base of the mountain and also engage in shamanic ritual. Indeed, Genghis Khan's success was seen as a sign that he was so blessed by Tengri that he was actually the embodiment of Tengri's will.

Burkhan Khaldun is one of, if not the, longest continually protected natural site in the world. Though it was revered before Genghis Khan's reign, Genghis Khan himself declared it a sacred site that must be protected. After his death, these decrees continued and it has been protected in one form or another ever since. The mountain is one of the most likely places of Genghis Khan's tomb, itself shrouded in mysticism.

Temujin united the Mongol clans and became Genghis Khan. Genghis Khan conquered the steppe, and in doing so created a vast trade and political system. He created an education system, was fascinated by new ideas and engineering; he politically empowered women throughout his empire. It was considered profane to spill the blood of nobles onto Eje, the earth mother. As such, there are several accounts of executions of nobility that adhered to this rule.

Genghis Khan considered himself an honorable man, and from his perspective, the wars he fought were justified by the disrespect shown to people he considered innocent. An example: Genghis Khan sent a letter to Shah Muhammed of Khwarazmia (present day Iran) describing the Shah as the ruler of the land of the setting sun and asking to open a trade route. Genghis Khan later sent a trade envoy of 500 Muslims. This envoy was captured by a governor of a region with Khwarazmia. In response, Genghis Khan sent a group of ambassadors (one of whom was also Muslim) to intercede with the Shah on the caravans behalf. The Shah had the Muslim ambassador beheaded, shaved the other two, sent them back to Genghis Khan, and ordered the execution of the entire trade caravan. At this news, Genghis Khan went to Burkhan Khaldun to pray about what to do.

So, yes, Genghis Khan was considered devout and holy, and his success was seen as an affirmation of his connection to Tengri and the other spirits.

More can always be said, but this AMA with Dr. Jack Weatherford for the release of his book Genghis Khan and the Quest for God might be of interest to you.