What is the ruling on praying in the private university prayer room, and what is the ruling on praying Asr in congregation an hour after the Adhan and an hour and a quarter before Maghrib?

It is prescribed that you be keen to perform the prayer in congregation at its appointed time to attain the reward of congregational prayer.

Delaying the Asr prayer by an hour after the Adhan or fifteen minutes before sunset is not sinful, as long as it does not take it out of its الضروري (necessary) time (when the sun turns yellow).

However, if delaying it results in it being performed during its الضروري time, some scholars consider it sinful if it was possible to perform it before that. Nevertheless, the prayer is considered valid because it was performed before its time definitively expired.

The الضروري time for Asr begins with the yellowing (of the sun), which is when you see the sun changing and yellowness appears on the ground and walls, meaning the sun is inclining towards setting.