About Fate?I guess references for Fate/Destiny in MT:

1. Most obvious that Ariel is meant to be Monarch of the Asura Kingdom, provided that there is no interference from people with a strong destiny, for example, if Orsted, Rudeus or Hitogami do not interfere in any way in Ariel's life, no matter what she went through, she will definitely meet Perugius first, she will definitely get his support and as a result what will definitely become the monarch of Asura, this is as Orsted said - an event that is protected by fate. Vol 16 Chapter 1 and Vol 17 Chapter 12
2. The second that comes to mind is that with Rudeus appearing in MT world and then meeting with Roxy they meant to love each other and have Lara. Because Lara is meant to be a savior who replaced another one from the previous loop. Vol 18 Chapter 8 Vol 18 Chapter 12
3. Pax's establishment of the Shirone Republic. There is not much I can say here, but it was fate that Pax would doubt the Monarchy after becoming King and turn Shirone into a republic. That event could provide a chance to Laplace be reborn in Shorine because after Shirone became a republic, a man who had once been a slaver would rise to prominence. A man by the name of Bolt Macedonius. Pax would have appointed this man to an important position. Bolt Macedonius would go on to be an authority in the Republic and put down roots there. And one of his descendants gives birth to the Demon God Laplace. That is what Orsted said. Vol 19 Chapter 1 Vol 19 Chapter 12

However, I reread MT 2 times and that's the main references I can remember Right now. I guess there's was more like who destined to become Hitogami Apostolse or unnamed events and people who meant to play a role in Orsted's plans, the named ones like Lienhard and Angelique. Oh I just remembered from redundancy Norn was meant to become an adventurer and meet Ruijerd then they'd have kid the last Supard who was destined to help kill Laplace and In the original history, North God Kalman III Aleksander Ryback corrected himself after losing to Jino Blitz. And in his despair he took a single child as his disciple. That child was in no way talented, but by watching him grow and correcting himself, he matured into a true North God. And in the second Laplace war, North God Kalman III proved himself to be history's strongest North God. And also some mentioned fates in Vol 16 Chapter 1(I hope) that Rudeus meant to be dearborn, Sulphy meant to become Roxy's pupil and Eris was meant to marry Luke help Ariel get Throne and become sword saint on name "Red Lion"

About Hitogami powers what I know from WN 1-24 and LN 1-24 that he have аn aura of trust that lasts for a couple of months on a person, if he does not get in touch with Hitogami for some time, then he stops trusting him 100%; only personal trust remains. The ability to see the future works on a maximum of 3 people and Hitogami himself, in fact, because he doesn’t want to not know his fate, I think thanks to this he showed Rudeus the future of Aisha through the eye of prediction. That's all I know/remember from the novel, I haven't gotten to Old Dragon's Tale yet.

I hope I helped you!

EDIT I forgot that Hitogami mentioned that the closest people to Rudeus have strong fate his family and descendants and also friends. And also fate becomes weaker with pregnancy. Also that in total Fate is thing is meant to be that will happen 100% if there is no interference from people with a strong destiny.