Is it permissible to allocate a short time (an hour or two) daily for studying the obligatory Islamic sciences, and to be occupied with other worldly studies, knowing that this year is the most crucial for determining one's academic future? And would that be considered a shortcoming?

A Muslim must learn about Tawhid (monotheism) and what negates it, how to perform purity (Tahara) and prayer (Salat) and what invalidates them, their pillars, conditions, and obligations. They must also learn the rulings of Zakat for those who possess wealth, the rulings of Hajj for those who can perform it, and the obligatory rulings of fasting before commencing it. This learning is an immediate obligation and should not be delayed. Studying concise works such as "Fiqh al-Ibadat" by Shaykh Ibn Uthaymeen is sufficient.