To me Szpilman seemed very concerned about his family. For example he saved his brother from the clutches of the Jewish ghetto police who had been rounding people up. Secondly he scoured the ghetto for a work permit for his father who was in danger of being deported without one. He also worked as a café pianist to earn money for food for his family rather than getting involved with the insurrectionists. Finally he was utterly devastated when his family were taken away by the Nazis. After that he was obviously concerned with his own survival. At another point in the film he tries to save a little boy who is crawling under the ghetto wall to escape from German pursuers.
I do not agree with your other point regarding Szpilman's detachment from the world when he mimes a piano piece while in hiding. Obviously we all understand that he is unable to actually play the piano as this would give away his hiding place. The fact that he performs this silent solo should be understood, in my reading of it, as a small escape from the nightmare he finds himself in and a connection to the life he has lost. From that perspective I completely see why he would do something like that.
I think Brody has skilfully portrayed a traumatized man who is numbed by the pain of what he has witnessed. The irony is that as he tries to hug the first returning war refugee to a destroyed city he is almost shot because he is wearing a German overcoat. The story about Szpilman returning to work at Polish Radio is not well explained in the film. The point was to reopen broadcasting at Warsaw Radio with exactly the same piece Szpilman was playing when broadcasting was interrupted at the beginning of hostilities in 1939. It's almost an as-I-was-saying-before-we-were-so-rudely-