Apple.ca accepts answer, Apple ID app/ iCloud doesn't?
If one web app works and another doesn't you would probably need to contact support to determine if the problem is with your account or with Apple's infrastructure. 

Also, you will want to be sure you are really connecting to Apple sites (some computers and networks are compromised by malicious software). If you are connecting to a site that is imitating / designed to look like Apple's, that could explain the acceptance of your answers as it would actually be collecting your account details. 


https://support.apple.com/en-us/HT204759 - phishing / verified Apple websites
https://support.apple.com/en-us/HT201487 - change back your actual password


In that case the "fake" approves your transaction to get you to keep trying all passwords you might reuse and then when you try a legitimate Apple site you are either locked out or the malicious people/software may have changed your password.