What is the exact message that you are seeing when trying to download an app ? Being asked for card details does not mean that you are being asked to pay for the apps, it's a way of confirming that you have a valid billing address in that country, and could be because you've moved countries (have you downloaded anything since moving countries ?). Depending upon what you are actually seeing and if you don't have a payment method for your country, then you could try contacting iTunes Support and see if they can stop the prompt : http://www.apple.com/support/itunes/contact/
As well as being tied to the account, all content, including apps, are tied to the country that they were downloaded in. For apps you might be able to redownload them for free - though they might show a price button against them in the store, people (who have moved countries) have posted that when clicking on the price they get a popup saying that they've already purchased the app and would they like to redownload it for free (as I haven't moved countries I can't confirm it).