emcampbe

There is no arrival lounge in Mumbai - since you will be connecting to a domestic segment, you'll clear customs after arriving from EWR and collect baggage, and have to re-check it prior to your next flight.

International and domestic flights at BOM are still in different terminals (with very few exceptions - mostly a few flights that have one flight number continuing into an international destination like AI 341 BOM-MAA-SIN).

If you are flying business on the domestic portion, you should have access to whatever lounge your carrier uses at the domestic terminal prior to that flight. Note (if you've never flown within India before) that you will need to show a copy of your itinerary along with a piece of photo ID (passport is best if you don't have an Indian type of Id) to security at the door before they will allow you into the terminal - they check this pretty well (this will be required for your return as well, both in HYD and BOM if you are doing the reverse route. Either have a printed or electronic copy ready (some say you need paper, but I have never had an issue showing an email confirmation or PDF on my phone).

Also note that domestic security in India is quite different than international security - you can bring liquids through and will not need to remove them from your bag - and after going through the metal detector will also be wanded no matter what. You also won't need any ID after checking in - but will need a tag for each piece of carry on luggage that you will get at the check in desk, it will be stamped once it clears security and that stamp will be checked before you can leave the security area and again after having your BP scanned at the gate.