Hello Nataliia33
It is difficult to give you a useful answer without knowing more details about your problems.
What kind of problems do you have with YouTube?
What kind of problems do you have with emails?
What strange questions about your name of your cat? You mean a security question for a lost password?
I believe to understand that your Apple ID has been compromised and hijacked, but that's just a guess from the few informations you wrote above.
If you think that someone is using your Apple ID then you should act quick and do the things below to check if you still have access to it.
First thing to do would be to change all your passwords, the first of them would be your Apple ID
to make sure you still have and keep access to your Apple account.
If this is not possible because you don't have your usual password working then you should contact the Apple Assistance to check if they are able to help you to gain access to your Apple ID again.
If you have ApplePay then you should monitor your credit cards stored there and in case there are strange movements block them immediately thru your bank.
Use a computer to check if you still have access to your social media accounts and other websites where you need a login and if you still can log in then change the passwords to make sure that you keep access to them.
However, please provide more and detailed informations about your problems so that we can understand what is going on.
As Dutchman already wrote, the English or your native speaking language community would be the better place to ask for help as there are more users understanding ans speaking your language.
Chris