Thanks in advance

I will be travelling from Hyd to Atlanta on July 18 2014
The following are my flight details

Hyd - Mumbai - Air India
Mumbai- Franfurt -Lufthansa
Frankfurt- Atlanta - Lufthansa

All the bookings are under a single ticket

Now, the following are my questions

1.) Do I need to check-in my baggage at hyd or mumbai?
2.) Will my Immigration be done at hyd or mumbai?
3.) Will the air india flight land in the domestic or international terminal?
4.) is it easy to switch between the terminals at mumbai?
5.) If checked at Hyd will air india ppl handover my baggage to lufthansa or i shall need to check-in again at the mumbai terminal

Please guide me