In the listed pages you will find some sources of publicly available data for India that I have come across or has been brought to my notice. They are available for download for free or by creating an account (e.g., Bhuvan/ICPSR). Even though the data are free, curating data takes a lot of time (and money) so please acknowledge (via correct citations) those who have made their data (and/or code) available and thus research possible. I also include links (italicized) to freely available open source software that I have some experience using and where I think they maybe required. And also lastly wherever possible, I try to include articles on understanding data generating processes.
Note: All errors are mine. If you notice any errors please email me at priyamvada[dot]trivedi[at]ashoka[dot]edu[dot]in. Also if you want me to include/exclude your name, please email me.