Download a Free App published only to India AppStore while my primary iTunes account is US Appstore?
You can have multiple accounts, you just have to log in and out to switch between them.

After you created an India account, log out of your US account: 


Settings -> App and iTunes Stores -> Apple ID -> Sign Out


Then sign in with your India account. Swipe close your AppStore app, then go into it again. Now you can download apps from your India account.