Tsunade's character might develop by becoming more maternal towards Naruto. Saving him could make her see him as more than just a village ninja. She could start to care for him in a more personal way, like a mother figure.
If Tsunade kisses Naruto, it could strengthen their relationship in a mentor - like way. Naruto might see it as a sign of deep respect and trust from Tsunade. He would likely feel more confident in following her guidance. For Tsunade, it could be a way of showing her pride in Naruto's growth.
Well, Naruto is known for his big heart. He might cook for Tsunade, just like he did for others in the village. While they eat, he could tell her funny stories about his adventures with his friends. His warm smile and friendly nature would slowly break through Tsunade's tough exterior. And he could also give her words of encouragement, like how important she is to the village and how much everyone looks up to her.
By teaching them her unique fighting style. Tsunade has a very distinct way of fighting that combines brute force with precision. The kunoichi can learn from her and adapt it to their own styles, making them more formidable opponents.
She could physically harm him. Maybe in a fit of anger, she punches or uses her strength on Jiraiya. Since Tsunade is known for her powerful physical attacks, it would be a likely way for her to hurt him. Another way is through emotional harm. She could reject Jiraiya's feelings for her in a very cruel way, saying things that cut deep into his self - esteem and his love for her.
She might become more fearless. Rescuing baby Naruto could put her in a dangerous situation, but coming out of it successfully could boost her confidence. She may start taking more risks in battles and leadership decisions, knowing that she has a responsibility to Naruto now.
Naruto might be initially confused. He trusts Tsunade, so being kidnapped by her would be completely unexpected. He would probably start by asking her why she's doing this.
Tsunade's character often develops a stronger sense of purpose. In fanfictions where she finds baby Naruto, she realizes that she has a new mission, which is to raise Naruto to be a great ninja. This might lead to her changing her ways in terms of leadership in the village. She might start to focus more on the future generation and how to make the village a better place for Naruto and others to grow up in. She also may become more empathetic towards others in the village as she experiences the joys and challenges of raising Naruto.
In many fanfictions, Naruto's determination and positive attitude start to rub off on Tsunade. She has been through a lot and is a bit jaded, but Naruto's energy makes her feel alive again. This new - found connection leads to a budding romantic relationship. For example, Naruto might bring her small gifts from his travels, which are simple but meaningful gestures that slowly warm Tsunade's heart.
If Naruto hypnotizes Tsunade, it could initially disrupt her leadership. She might make uncharacteristic decisions that could throw the village into chaos. For example, she could start allocating resources in a strange way.