Is it permissible for this Muslim girl to do her graduation project in a European country, taking into account the Sharia guidelines, given the availability of better opportunities in her field of study there, and the fact that there isn't a significant difference in the issue of mixing (of genders) compared to her home country?

It is not permissible for a woman to travel to a European country to complete her studies, as there is no necessity that permits travel to lands of disbelief and corruption. The dangers of traveling to the lands of the polytheists are numerous, among them the open display of disbelief, immorality, and disobedience. This is warned against by the Prophet's (peace be upon him) saying: "I am innocent of any Muslim who resides among the polytheists," which was interpreted as: "Their fires should not be seen by one another."