Well you are right Applejuiced, the situation is really weird, i understand that completely. Thats why i first want to gather information before calling the service,
i dont want to sound crazy when i do.
It's really simple situation in reallity. I registered three times and erased the phone three times to start again.
Absolutely, i do admit it is my fault. I also shouldn't have let other people (cousin), to try fixing things up. But the wrong is done there is no turning back. I am searching for an options of what can be done, obviously the only thing now would be calling the Apple service

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In worst case scenario, i will simply sign in though different email provider (yahoo, gmail). as if i understood right i will be able to do that as long as i provide personal credit card.
But i still can't find the answer to if another person (in my case cousin) did sign in with his account, can he somehow compromise my iphone (like install something remotely or so on) becuase something similar did happen once to my android device's gmail that i used to share with friend. And if i erased and reset everything after that would clear any connection with him and his account?