How can I make up for the Dhuhr and Asr prayers I missed due to university studies, and does this require the intention of making them up later, or should they be performed directly with the opening Takbir (Takbirat al-Ihram)?

Prayer is a great pillar of Islam, and it must be performed at its prescribed time. Deliberately delaying a prayer beyond its time without a valid Shar’i excuse is a major sin. If you are unable to perform Dhuhr prayer at its time at the university, it is permissible to combine it with Asr prayer as a delayed combination (jam’ ta'kheer) if there is a need or hardship, provided that it does not exceed the time of Asr, which ends at sunset. When making up a missed prayer, it is sufficient to specify the prayer by intention at the time of the opening takbeer.