Is it permissible for a girl to travel for study or work without a mahram, and is the father sinful if he refuses to travel with his daughter due to his preoccupations, and is it then permissible for her to travel? And how does one accept Allah's judgment and get rid of the feeling of inner dissatisfaction, and is one sinful if perplexed by a legal ruling and does not research it for fear of finding out it is haram?

The majority of scholars hold that it is not permissible for a woman to travel without a mahram, except in cases of necessity. Some scholars permit it when there is no fear of fitna (temptation/strife), especially if she is accompanied by other women. Therefore, you should not travel without a mahram, and your father incurs no sin for refusing to travel with you. If you cannot find a mahram, do not travel for study or work. A Muslim must accept Allah's decree with an open heart, and this is achieved by rectifying the heart and strengthening faith through righteous deeds and beneficial knowledge. Ibn al-Qayyim said: "And whenever the heart is permeated with the cheerfulness of faith... it receives the rulings of the Lord, the Exalted, with a vast, open, submissive heart: for it has accepted with complete satisfaction this religious decree, which is beloved to Allah and His Messenger." Among the means of rectifying the heart and strengthening faith are: knowing Allah through His names and attributes, reflecting on His blessings, pondering the Quran, knowing the Prophetic Sunnah, and frequently remembering death and the hereafter, as well as engaging in dhikr (remembrance of Allah) and du'a (supplication). It is not permissible for a mukallaf (accountable person) to undertake an action whose permissibility is doubted before knowing Allah's ruling on it, based on the words of Allah Almighty: {And do not pursue that of which you have no knowledge} [Quran 17:36].