How do you buy a ringtone, without using security questions? How can I buy a ringtone for my iPhone with my debit card?

If you are being asked for their answers then you can't. If you don't remember them and you have a rescue email address (which is not the same thing as an alternate email address) set up on your account then go to https://appleid.apple.com/ and click 'Manage your Apple ID' on the right-hand side of that page and log into your account. Then click on 'Password and Security' on the left-hand side of that page and on the right-hand side you should see an option to send security question reset info to your rescue email address.

If you don't have a rescue email address (you won't be able to add one until you can answer 2 of your questions) then you won't get the reset option - you will need to contact iTunes Support / Apple to get the questions reset.

Contacting Apple about account security : http://support.apple.com/kb/HT5699

When they've been reset (and if you don't already have a rescue email address) you can then use the steps half-way down this page to add a rescue email address for potential future use : http://support.apple.com/kb/HT5312

For the debit card, as far as I know they are no longer accepted as a valid payment method - they are not listed on this page and there have been a number of posts recently about them being declined. So if you try to use a debit card you may get an error message.