Is it permissible for a female student in medical school to attend private lessons with a non-Muslim doctor, knowing that the lessons may exceed three consecutive hours, which would lead to missing prayers, and can she combine prayers or ask permission to perform the prayers without neglecting her obligations?

The basic principle is to observe prayer at its appointed time. However, if considerable harm is incurred by performing each prayer at its time, then it is permissible to combine Dhuhr and Asr, and Maghrib and Isha, out of necessity, if seeking permission more than once would harm you. As for delaying the Asr prayer until the time for Maghrib begins, this is not permissible under any circumstances. It is obligatory to observe prayer and prioritize it over all else.