Whether you pay in advance or pay on the day of travel will depend solely on your airline's agreement with AZ. Payment, however, is always made at the time the ticket is issued (I've never seen otherwise).

Most ID agreements (whether they be ZED or ID90) are self-ticketing, meaning the employing airline (your airline) issues the ticket for you to travel on the other airline's flights. In such cases, you would pay your airline to have the ticket issued. A few carriers have agreements that will allow the employee of another airline to walk up to its ticket counters to purchase a ticket for travle on its services. These are arranged primarily with airlines that do not interline passengers (e.g., B6 or WN). You would pay then. Again, at the time the ticket is issued.

Based on the fares published by these two airlines, I would guess your discounted fare would be somewhere around $1000, probably not more. Keep in mind that AZ does not operate LON-BOM-NYC, you will need to connect via MXP in both directions.

Best of luck.