Q: use real or fake birth date

Don't be silly.  You need to use your real date of birth and your Apple id is secure when you set it up as you have a password, so nobody can forward and get into your Apple id.

You need to use real details or certain things could be voided if you lie about it on purpose.

If you are that worried, then enable two step verification - Frequently asked questions about two-step verification for Apple ID - Apple Support

You need to remember what your security questions are then don't you?

That is ultimately up to you if you want to use a real or fake birth date but remember when verifying your identity down the road that you remember what you put down as your birth date. People who figured out my security questions have accessed my email before to reset my password. Just saying.

If they know your password and can guess your questions they don't need Apple or anyone else to change your password from the AppleID management web site. KEEP YOUR PASSWORD PRIVATE! and use a strong password. And as I said, use two step verification for added security. With 2-step verification, you need MORE than just your password to change anything, and security questions are no longer used at all.