If Naruto had Esdeath's powers, the plot would change drastically. Naruto's usual jutsu-based combat would be replaced by Esdeath's ice powers. His fights would be more one - sided as Esdeath's powers are extremely powerful. For example, in battles against Akatsuki members, he could freeze them instantly instead of engaging in long - drawn - out battles. Also, his relationships with his friends might change as his new powers could make some of them fear or envy him.
Naruto would gain some really cool (pun intended) new abilities. The ice - making ability would be the most prominent. He could form ice clones, similar to his shadow clones but with the added advantage of being made of ice and potentially having more durability. His sensory abilities might also be enhanced, as Esdeath has a good sense of her surroundings when using her powers. He could detect enemies hidden in the ice or snow. And, like I said before, the time - freezing power. This would allow him to analyze his opponents' moves during the frozen time and come up with the perfect counter - attack. It would add a whole new dimension to his combat skills.
Tatsumi is very likely to be involved as he has a significant relationship with Esdeath in the original story. Her subordinates in the Jaegers might also be part of the fanfic. They could be shown as being protective or having mixed feelings about her pregnancy.
If Naruto is Esdeath's brother in fanfiction, they could embark on adventures across different dimensions. Since Naruto has experience with his own world and Esdeath with hers, they could explore new lands together. They might encounter strange creatures and powerful enemies. Along the way, they could learn from each other's fighting styles and abilities, Naruto teaching Esdeath about chakra and she teaching him about her own brand of combat techniques. And they could also be on a quest to reunite their fragmented family or uncover a long - hidden family secret that has the power to change their worlds.
In certain fanfiction works, Tatsumi is indeed made into Esdeath's pet. This can be a way for writers to explore darker or more extreme versions of their relationship. It might involve Esdeath treating Tatsumi in a demeaning way at times, or it could also lead to a strange form of affection developing between them as the story progresses. It really varies from one fanfic to another.
Esdeath's demise in the manga is quite intense. It's a culmination of her actions and the circumstances she finds herself in. To get the full impact, you really need to delve into the manga pages.
Some characters might adapt well due to their own desires for power. For example, Sasuke could see the peerage system as a means to gain more strength to achieve his revenge. He would likely be drawn to Esdeath's strength and might be willing to submit to her in order to learn from her combat skills.