Why I can't download any free app without credit card once the money's gone off the card

As far as I know, unless you specifically created the Apple ID using the exact steps required by Apple to have an iTunes account without using a credit card, you will have to make sure that you have at least some funds available in this account in order to even download free apps.

You have already created an ID that had a card associated with it, so unless you are able to remove it in your account details, you have to keep it updated in order to keep using this ID.

See if you can remove the card from your account now. Settings>iTunes and App Store. Tap your Apple ID. Tap View Apple ID. Enter your password. Go to the Payment Information field and tap on it. See if you can select "None" in the next window to remove the card. If you can do that, you may be able to download free apps now.

Whenever you attempt to perform a download for teh iTunes app store, it will place a $1 USD hold against the credit card registered with the account. If your account has no funds avaialable, then that hold will fail, and the download will not be allowed (even updates to apps already purchased). This hold is never submitted to your credit card company, and after the default time period (3 or 5 days I believe) the hold expires, and the funds become immediately available in your credit card account again. This is the same technique that most gas stations use for pay-at-the pump purchases, except that once your transaction is completed, the gas station submits the purchase in the actual amount of your fuel purchase.