The machine doesn't translate idiomatic expressions, which is what these are.
creerse el ombligo del mundo
ser muy suyo
= To keep to oneself. (to be reserved, to be introverted)
= To be a character. (meaning such a person is hard to figure out - usually said, "What a character.")
= That's just like him/her. (strange/reserved behavior is characteristic of the person)
= S/He's a law unto herself/himself.