I'm pretty sure you can buy in Indiana with an Illinois ID if you buy from an FFL. But they must ship it to Illinois for you to pick up. But I am not up on such things and avoid doing things I am not absolutely certain are legal.
My store will NOT sell a handgun to an out of state resident. IF he came in with an IN ID and IN address then that is essentially (for our purposes at least) establishing IN residency. A couple weeks ago we had a KY resident who wanted to purchase a handgun and that was killed real quick. My sales guy suggested we sell it and then ship to a KY FFL and my boss said we can't do that anymore. We offered the option of purchasing the same gun online and having it shipped to a store in KY though. I know the ATF accepts a student in another state for school as establishing a sort of residency but we need documentation to complete the sale. Usually when we go to BPS we head north so we're still in IN so we don't have to worry about legality if we see a gun we want. That scored me a gun for well under half it's value.