I have had the same problem. Set up an account probably over 10 years ago, no idea about answers to the security questions or password. Managed to reset the password, but when signing in it asks for 2x security question answers. In knowing neither, it offers an option to reset the security questions. But low and behold, it asks for a security question to reset your security questions -> wow Apple that is the most incredible example of idiocy.
Thinking cooler heads would prevail over the phone I called their support centre, and what did they ask... what are the answers to your security questions!!!! I asked him point blank, if I do not know the answers to the security questions to reset my security questions, and I am the sole user of this account, then surely you are pointedly locking up my account in perpetuity, to which the service agent said yes I would never be able to use the account again unless I can remember the answers to my security questions.
Phenomenal incompetency of the highest order Apple, for one of the world's richest companies you would have thought they could have employed some logic.
