FWIW one of the Plaza Premium arrivals lounges is open. It's pretty barebones, you get seating & power points to charge devices, and a round of tea/coffee/soft drinks. They 'limit' you to three hours on a priority pass, but you can re-swipe your card after three hours if you need to wait longer. They also have nap rooms in that lounge, but it's not included with priority pass, IIRC the nap rooms were ~Rs 3000 for 3 hours the last time I was there.

The lounge is landside, you turn left after you exit customs and it's right there.

There is a holiday inn express inside the airport that you can book by the hour. There are a few threads on this forum about that hotel.

Domestic check-in opens 4 hours before the flight. IME if the CISF security guards allow you to enter the check-in area (4 hours before the flight), UK will let you check-in. Once you check-in you can access the better Priority Pass and AMEX lounges that are airside.