One idea for a Naruto vs Todoroki fanfic could be that they are brought into a strange new dimension by some sort of magical entity. Naruto starts off with his usual energetic self, trying to figure out what's going on. Todoroki, on the other hand, is more cautious. Naruto might start with a simple Rasengan attack, but Todoroki uses his ice side to block it. As the battle progresses, Naruto realizes he needs to up his game and taps into his Nine - Tails chakra. Todoroki then decides to combine his ice and fire powers in an attempt to counter Naruto's new - found strength.
The most exciting scenario would be when Naruto goes full Nine - Tails mode and Todoroki uses his maximum ice and fire combination. Naruto in Nine - Tails mode is extremely powerful, with his chakra radiating and his physical abilities enhanced. Todoroki, when he combines his ice and fire, can create a powerful and unpredictable force. The clash between Naruto's brute strength and Todoroki's elemental control would be visually stunning and full of intense action. The environment around them would be completely transformed, with the ice melting and the ground shaking from Naruto's power.
Fujiko Fujio had created many works in his life, and one of the most famous works was Doraemon. Other than Doraemon, he also created Doraemon, Random Door, Bamboo Dragonfly, and other classic works.
His friends would probably take care of him. Midoriya would be very eager to help, using his kind-hearted nature. He would make sure Todoroki is fed and comfortable.
One idea could be that all his friends at UA plan a surprise birthday party for him. They decorate the common room with his favorite colors, blue and red. Another plot could be Todoroki spending his birthday with his family, trying to reconcile with his father on this special day. Maybe he receives a heartfelt gift from his mother that has a deep emotional significance.