I am new to Apple/iOS. I want to install a free application from iTunes (ex. Flipkart).
But I don't want to share my Credit card information in iTunes. Is there anyways to download application from Apple stores without iTunes?
I'm afraid not. The only legal and legitimate place to obtain iOS apps is the App Store.
Try this if you do not already have an iTunes account. Go to the App Store and attempt to download the free app. You will get a pop up asking you to sign into an existing account or set up a new account. Choose to set up a new account. When you get to the part about adding a payment method, select none. If this works, you'll be able to download the free app. If, in the future, you want to buy a paid app, you can add an iTunes gift card to your account. If you don't get the option to select none as a payment method you'll have to add a credit card to your account. You'll still have the option of using iTunes gift cards to pay for iTunes and App Store purchases.
BTW, the iTunes, App Store, and Apple online store are some of the most secure places to use your credit card while shopping online.