I will arrive to Bombay airport at 11:00 pm and my flight is the next day at 6:00 pm. Can i spend that time in the airport waiting room? Is there any problem for safety?
The to-go guide for these question is http://www.sleepinginairports.net/asia/bombay.htm this website. It would seem from these reviews there shouldn't be a problem except it might be uncomfortable even for an airport.
You can easily spend that time at the airport. There are multiple lounges, and some are even open 24/7.
If you really want to spend your time relaxed; try the pranaam lounge - a 6 hour pass will cost between 45 and 55 USD.
Your credit card may also grant you access to the loyalty lounge at Terminal 2.