You might be interested in this earlier answer of mine on trade between pre-modern China and India. The first part looks more generally at trade from Europe and eastern Africa via India to China, which can be traced at the very least to the 9th c. The second part turns to the more limited direct India-China trade, going back to approximately the 13th c. I can't really comment on other forms of contact between both regions, although the transmission of Buddhism to and later from China comes to mind as another important connection (esp. since Buddhism subsequently declined in importance in India). As I mention in the post, stronger isolationist policies by Chinese emperors strongly impeded direct contact with India, including trade, from the 15th c. onwards.