Are the amounts paid to teachers in exchange for success considered permissible or impermissible, knowing the female student's diligence in her studies?

What your father paid is a forbidden bribe, unless not paying it would result in injustice to you and there is no way to prevent it except by paying a bribe, and provided that it does not result in injustice to others. It is better to avoid paying bribes, as the Prophet, peace and blessings be upon him, said: "The curse of Allah is upon the briber and the bribed." You are permitted to continue your studies as long as there is no legal impediment, such as impermissible mixing [of genders] or forbidden seclusion [khalwa].