Is it permissible to work as a domestic helper for non-Muslims in Europe, knowing that the questioner is compelled to work to finance her studies and can find no other work besides this, after having previously worked in a restaurant that served alcohol and left it due to its prohibition?

It is not permissible for a Muslim to work as a personal servant for a disbeliever, especially for a woman residing in a disbelieving country, due to the temptation and danger involved. Therefore, it is preferable to seek another permissible job, or for the father to provide for his daughter, or for her to marry a righteous man who can support her. It is also preferable to strive to return to a Muslim country to complete her studies. If this is not possible, and you are in dire need of work and can find no other, and you are secure in your person and your religion, then there is no objection to taking it out of necessity, with the obligation to leave it as soon as an alternative is found.