While I can somewhat picture life in Europe, the Middle East and China during the middle ages, I feel like I know next to nothing about medieval India. So how was life and the culture like in India at that time? I know it is a broad question, so I am mainly looking for a brief introduction and some possibly some suggestion for more literature on the field.
As you say, this is both a huge area and time-span you're asking about - in early medieval South Asia ("India" is often used for a later time period) there were various competing Hindu realms - amongst others the Mauryas and Guptas - whose influences changed over time, with increasing predominance of Muslim sultanates towards the (in European terminology) Late Middle Ages. For an introduction it might be a good idea to start with literature - Kulke's and Rothermund's "History of India" is very concise and apparently available online, with two chapters on medieval South Asia. Another good place to start is Burton Stein's "History of India", as he's a specialist on pre-modern South Asia and its state formation.
Hope that helps. For something more specific, here's a link to an earlier answer of mine on the Late Medieval Hindu realm Vijayanagara (14th-17th c.). Especially the second answer deals more generally with social and political organisation and might be of interest.