One common theme is the exploration of her family relationships. Given the complex family dynamic in the original MHA story, fanfics often delve deeper into how her relationship with her father or siblings might develop. Another theme is her growth as a hero. Writers like to show how she overcomes challenges and hones her skills.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are numerous MHA fanfics there, and you can specifically search for those related to the female Todoroki character. Another option is FanFiction.net, which also has a wide range of stories. Just use the search bar and type in relevant keywords like 'MHA female Todoroki' to narrow down your results.
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.
Todoroki's character development in time travel fanfictions can be quite profound. He may start as a somewhat aloof character, but through time travel, he begins to understand the importance of relationships more deeply. When he travels back and witnesses the relationships he could have had or lost, it makes him cherish the ones he has in his original timeline. His view of heroism also evolves. He realizes that being a hero isn't just about using his powers but also about making the right choices at the right time, which is especially highlighted when he has to make decisions that could change entire timelines.