What is the ruling on doubt, obsessive thoughts, and fear of not succeeding in studies and work, and seeking success in supplication while committing some sins, such as listening to music, and do sins delay relief?

Allah has placed contentment and joy in His obedience and the fulfillment of His commands, and He has placed worry and sorrow in the neglect of obedience and the commission of sins. Thus, most of the distress, grief, and constriction that afflicts a person is the fruit of sins.

If you wish to be free from your current state, then adhere to the obedience of your Lord, persevere in His worship and remembrance, and know that what has befallen you is only by Allah's decree and destiny. Therefore, embrace contentment with your Lord's decree, and it will fill your heart with satisfaction and joy. Do not despair of Allah's mercy.

Seeking forgiveness is a means to attain the good of both this world and the Hereafter. You can supplicate for ease in affairs and for beneficial knowledge, while also taking the necessary means to acquire learning.