Where can I find current prices for RTW out of India?

If I plan 4 Continent - Asia, Australia, South America, North America, does the flight from Chicago - Bombay with change of plane (and carrier) in London legal?

Here are my plans

BOM-HKG-NRT-SYD-EZE-ORD-BOM.
Any thoughts how I can maximize this? I am constrained by time...