yes, Kumon is healed, but like he said he had nothing to eat or drink for about one day, he has the mental trauma from being cut and don't forget, contrary to her he is just a beginner swordsman without any armor or weapon, so counting him in need of protection is actually quite reasonable
for her to just do everything, yeah it's a bit crazy, they could have made her a college student becoming a doctor or the like, that would make her more believable, but hell, there are a lot of way more unbelievable mc's out there, at least they are trying to make it realistic, letting her think about the required steps and get experience at the hospital, nearly all magic users just cast heal and everything is fine,