Transit in CCU will be easy, just buy the Indigo or Air India ticket separately. The SQ flight lands around 10pm, the DMU flights leave next morning, so you have enough time to go thru immigration and 'enter' India.

CCU has 'retiring rooms' in the terminal you can use to wait for your next flight since checkin doesn't open till about 4 hours before your flight: https://www.kolkatainternationalairp.../retiring_room Sadly you can't book them in advance, but they should have space available for SQ arrivals.

DMU no longer needs any permits for foreigners: https://dimapur.nic.in/tourist-information/ The line permit thing is for Indians.