Sprint is a mobile network operator in the states. I don't think it is related to your issue.
Sprint is a telecommunications company, not just a mobile operator. They actually operate a 100G backbone between Australia and India (Perth to Mumbai via the SWE3 cable), so grand-parents question isn't that unreasonable.
Almost all undersea cables are owned by consortiums that are responsible for installation and ongoing maintenance. Telecoms like Sprint or Level 3 buy fiber pairs and run the gear on each end.
You can test for it by sending typical files over http (aka download) and then skyping and compare the bandwidth. Or the other way round. Run a few tests over a few days. This won't tell you whether Sprint is behind this, however you will be able to know whether Skype is affected. If yes, you could try to tunnel the Skype traffic over ssh. If ssh traffic is not throttled you should experience better throughputs.
Yes, something in india is limiting your connection most likely. Whether it be network speeds or something else, the servers in Australia are super fast