Recent Update

First of all, thanks to all of you who tried to respond with the best data they had, Over the years, the process has changed many times and hence best to get recent datapoint.

Data from friend's trip last week:
1) bags are collected by the respective airline after customs (make left). It helps to have both domestic and international flights on the same PNR for much better baggage allowance
2) This area at new BOM INTL terminal is far superior to old one
3) You are NOT allowed to take elevator to the departure area (even the semi-secured check-in area) by CISF
4) Even in the middle of night, shuttle departs every 10 minutes and they get filled pretty quickly
5) You DO NOT have to carry your check-in luggage on these shuttles - only carry-on
(Note that this contrasts process from several years ago)
6) There is an entrance to Niranta Hotel (airport transit hotel) near Shuttle waiting area
7) You can check-in your bags at these counters at INTL terminal only if your domestic connection is within next 12 hours.
8) Domestic terminal has not improved much in many years (which should be expected as it is slated to be downgraded to LCC use only with next few months)
9) You are still better off going to domestic terminal sooner rather than hanging around at INTL terminal because there are lot more shops open even in middle of night (THIS IS NEW INFORMATION CONTRADICTING posts here in this thread). Electronioc shop, gift shop, luggage shop, etc. are open. More than one coffee shop open. ( BTW, they do sell lot of food items, not just tea/coffee.
10) Lots of people waiting for their connection at domestic airport even at 2am or 4 am. So you are not lonely at all. (Mosquitoes are omnipresent between Oct-Feb and disappear during summer months.
11) There are charging stations but just like any airport in the world, supply-demand factor is out of whack. Carry battery pack but make sure to never to put them in checked luggage.
12) No one asked for any tips at any point (immigration, bags collection, customs, transfer shuttle) Pretty professional straightforward process.
13) Both terminals are air-conditioned but westerners may find it weak

Funny note: On this particular case, pax were bused to connecting plane which was parked within 200 ft of 9w flight that arrived from BRU!!!

Hopefully, 9w will soon follow AI to move domestic flights to INTL terminal and then we can retire this thread.