Is it permissible for my sister to travel to America for an educational study mission lasting 4-5 weeks, knowing that she will reside in a dormitory designated for girls only, and her interactions with males will be formal at the university?

Your sister is not permitted to travel except with a mahram. She is also absolutely forbidden from traveling to disbelieving countries if she will not be able to observe the rituals of her religion there. If she does travel, she must adhere to the Islamic dress code and Islamic manners in her interactions with her colleagues in her studies. If she predominantly believes that the travel will lead to unlawful mixing, then it is not permissible.