what might an observant Chinese traveler from the Han dynasty era find surprising or offensive in India or the Greco-Roman world? What similarities might he or she notice?

Similarities

China during the Han dynasty had very structured social hierarchies, with twenty different classes. This somewhat resembled the caste system of India. Arranged marriages were the norm, as was the case in India. Also, divorces were allowed just like in the Greco-Roman world. Social and economic activities were highly gendered in all three countries. Philosophy, arts and literature were very developed in all three cultures.

Differences

Buddhist ideas were adopted during this period, which were very different from the religious traditions of the other regions. The Chinese government was highly centralized, while the Greek city-states were closer to a democratic, federal institution. Culinary traditions were very different among the regions because of their different weather.