Is extra-cocurricular activities important to apply to UK and/or USA universities?

Yes. Colleges like to see if you can work with people, and if you have any special skills.

I fail to see what taking A levels privately has to do with what you do in your spare time. Yes, doing nothing except study will affect your chances.It suggests that you're working at your maximum capability just to get to A level standard, and have no chance of stepping up to the next level.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.