Is it permissible for a woman to travel without a mahram to complete her studies in Mecca, and to leave a country that she considers to be a land of innovation and mixed society, and is this journey considered a journey of obedience?

A woman is not permitted to travel to seek knowledge without a mahram, due to the Prophet's (peace and blessings be upon him) saying: "A woman shall not travel except with a mahram." This includes traveling to seek knowledge. A woman can seek knowledge in her own country or online, as many lessons and lectures are available to facilitate this.