Unauthorized password reset attempts on old Apple Account

Thank you for your help. I now understand that the way to resolve this issue is to log in to my account from one of my Apple devices. From there, I can add two-step verification for my phone number, which will allow me to regain access to my ID and redo everything.

It was a bit unclear that I couldn't add two-step verification directly from my internet browser (which caused the issue I said earlier) and had to use an Apple device. I was a little hesitant to use my Apple device since this account seemed compromised, but thankfully the hacker hasn't breached my password yet.

See this on how to regain control of the account

1. Change your Apple Account password. Make sure that you use a strong and unique password.
2. If you can't change your Apple Account password because it's already been changed by someone else, reset your password.
3. Go to account.apple.com to update any of personal or security information that isn't correct or that you don't recognize.
4. On account.apple.com, select Devices and remove any devices associated with your Apple Account that you don't recognize.
5. Check with your email provider and cellular carrier to make sure that you control every email address and phone number associated with your Apple Account. For example, check with your cellular carrier that SMS forwarding hasn't been set up for a phone number associated with your Apple Account. 

If you think your Apple Account has been compromised - Apple Support

erlangen wrote:

The problem is that whenever I login and try to access my account.apple.com, i got message "You have made too many attempts to answer your security questions. You can try again later." and I have no way to view anything on account.apple.com related to my account, I already reset my password but someone else is still trying to maliciously reset my password and answer my security question and lock me out. Anyway to block these kind of malicious reset?

Yes, you have to turn on Two Factor Authentication. Security Questions have not been recommended for a long time. With Two Factor Authentication, there are no Security Questions that can be guessed incorrectly and in order for someone to access your account, they need the Verification Code sent to your device or Trusted Phone Number that you would set up when turning on Two Factor Authentication.

The problem is that whenever I login and try to access my account.apple.com, i got message "You have made too many attempts to answer your security questions. You can try again later." and I have no way to view anything on account.apple.com related to my account, I already reset my password but someone else is still trying to maliciously reset my password and answer my security question and lock me out. Anyway to block these kind of malicious reset?