To answer your second question, European commoners, or anyone really, in the medieval period would have a rather spotty knowledge, if at all, of demographics across Eurasia.

As for your first question, the size and age of these places is well known, and were, since Alexander the Great's time, major destinations for travel and trade.

I've found it helpful to look at the long duree of Eurasian history as having interlinked cultural regions, 5-6 major regions with smaller hubs.

The 6 regions are Europe including western Russia; China and East Asia generally; India including Pakistan and Bangladesh; the Middle East and North Africa; Southeast Asia; the islands of Indonesia, Phillipines, etc.; and the Eurasian Steppe.

These hubs are influenced by one another, and have had movements of people and culture, but tend to coalesce into these broader regions.

So, to answer your question, 'India' was traditionally a concept like 'Europe.' A broad cultural identity In a geographic space. The is unlike China, which was itself a state for most of this time even if divided internally.