1. If you do not fly a segment of a ticket, the remainder of your ticket will auto-cancel and have no value. You run the risk that it will not be reinstated and that you are required to purchase the onward/return segments back to BOM. Thus, if you do not fly the segment due to the change or a cancellation or delay, make certain that the segment is cancelled and that you confirm, after the fact, that the remainder of your itinerary is still intact.
2. If you still wish to fly, your options are to fly earlier or later and CX, as the ticketing carrier, will have to make all of this happen. As noted, you are not entitled to and are extraordinarily unlikely to be issued vouchers or a reimbursement for the hotel rooms should you choose to fly in the night before.
3. Lots of travel options xPHX. I can't conceive of a taxi.