Well, in the fanfic, Anakin's skills would be a huge asset or a threat to the First Order. If he decides to join them, his combat abilities and knowledge of the Force could make the First Order even more powerful. However, if he realizes that they are on a wrong path, like the Sith - influenced path he once walked, he might use his skills to undermine the First Order from within. He could start by influencing the stormtroopers, showing them that there are other ways than blind obedience.
Well, he could either try to take over the First Order with his powerful Force abilities. Maybe he would see it as a new tool to gain more power and control in the galaxy.
Some in the First Order could see him as an opportunity. They might think that his skills and knowledge could be used to strengthen their military might. However, others could be suspicious, especially those who are power - hungry themselves and see Anakin as a rival for leadership within the organization.
The First Order's higher - ups, like General Hux, would likely be suspicious of Anakin. They wouldn't want someone with so much power and an unknown agenda running around. They might try to keep an eye on him, or even plot to get rid of him if they think he's going to disrupt their plans for galactic domination.
There could be a hermit or an outcast Jedi or Sith on Dathomir. Anakin meeting this character could lead to a great revelation. Maybe this character has been in hiding on Dathomir for years, observing the balance of the Force there, and Anakin's arrival disrupts that balance and forces an interaction that changes Anakin's perspective on many things.
Well, one possibility could be that Anakin goes to Dathomir in search of some unique Force knowledge. Maybe he's heard rumors about ancient Sith secrets there.
The Jedi would be the most directly affected. They wouldn't be massacred, and their order could continue to thrive. Also, the clones would be affected as they wouldn't have to carry out the unjust order. And of course, Anakin himself would be on a different path, likely seen as a hero rather than a villain. Padmé might also be affected as she wouldn't have to witness Anakin's fall to the dark side.
Well, if Anakin stops Order 66 in the fanfic, it would mean that the Clone Troopers wouldn't turn on the Jedi. Anakin might have a change of heart after realizing the full implications of what Palpatine was asking him to do. He could then warn the Jedi Council. This would completely change the course of the Star Wars saga. The relationship between the Jedi, the clones, and the Republic would be very different, and there would be a whole new set of stories to tell about their future together.
One possible plot could be Anakin going back to a time before his fall to the dark side. He could use his knowledge of the future to prevent certain tragedies. For example, he might stop the Clone Wars from starting, thus saving countless lives. This would also give him a chance to redeem himself and perhaps even change the fate of the Jedi Order.
Anakin could encounter future versions of his friends or enemies from the past. For instance, he could run into a future version of Obi - Wan Kenobi who has also somehow traveled to that future time. Or perhaps he meets a new generation of Sith who have different motives and methods compared to the Sith he knew in his own time. They could challenge his understanding of the dark side and the Force in general.