Certainly this was a University, even metallurgy lab has been found in Nalanda. Many chinese Scholars use to come to Nalanda and Study, we know this because of their notes and their day to day life in the university. Xuanzang lived in Nalanda for about 15 yrs and studies and he noted a lot of things in his notes. He even explains about Brushing the teeth and morning cleansing rituals. Like how too do bowel and clean the hands. How to use the toilet etc. And when he returned he took bak 10000 Books back with him.