Is it permissible to combine prayers (Fajr, Dhuhr, and Asr) in the morning, then (Maghrib and Isha) upon returning, given the absence of a prayer area at the place of study?

It is not permissible to perform the Dhuhr and Asr prayers in the morning. Each prayer must be performed at its legally prescribed time. Prayer does not require a specific location like mosques; rather, it can be performed anywhere clean, as the Prophet, peace and blessings be upon him, said: "The earth has been made for me a mosque and a means of purification, so wherever a man from my Ummah is overtaken by prayer, he should pray." If the distance between the two cities is a travel distance (83 km or more), you are permitted to combine Dhuhr and Asr, and Maghrib and Isha, and it is permissible to shorten the four-rak'ah prayers to two rak'ahs as long as you are traveling.