How can I achieve devotion (khushu') in prayer and ensure its acceptance, while also maintaining the regular Sunnah prayers (Sunan al-Rawatib)? And am I sinful for delaying the Dhuhr prayer past its prescribed time due to school and transportation circumstances?

Grief and worry dissipate by adhering to obedience to Allah, striving in His worship, and drawing closer to Him. This is achieved by consistently performing a small deed and gradually increasing it, and by organizing time between studies and acts of worship.

One must also strive in supplication and resort to Allah, and struggle against oneself to adhere to righteous deeds, for the pleasure of worship is only attained through struggle.

Means for achieving khushu' (devotional humility) in prayer are explained in previous fatwas.

As for the Dhuhr prayer, it is permissible to delay it as long as it is performed before the entry of the 'Asr time. Otherwise, it is not permissible, and you must find a way to perform it on time. If that is not possible, some scholars have permitted combining prayers out of necessity, provided it does not become a habit.