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BTW, once an account is set-up it is necessary to have a valid form of payment associated with your account whether you purchase free apps or not.
I have heard that connecting to your itunes account on a pc allows you to change it to None but have never tried and all examples for it only show for new acoount not one already set-up.
Your Apple ID is apparently set up to require a valid form of payment. If you are downloading free apps you will not be charged. But a debit card is no longer a valid form of payment and that is why you are being asked for payment info when you try to download an app.
This link is to an Apple support page with a list of valid forms of payment: http://support.apple.com/kb/HT5552
The easiest is a credit card. But if you don't want to use a credit card purchase an iTunes gift card and enter that.
Change you form of payment with the Settings app.
Settings > iTunes and App Store > tap on your Apple ID > View Apple ID > Enter your Apple ID password > tap on payment information and change it there.