Should '#include' and 'using' statements be repeated in both header and implementation files (C++)?

I'm fairly new to C++, but my understanding is that a #include statement will essentially just dump the contents of the #included file into the location of that statement. This means that if I have a number of '#include' and 'using' statements in my header file, my implementation file can just #include the header file, and the compiler won't mind if I don't repeat the other statements.

What about people though?

My main concern is that if I don't repeat the '#include', 'using', and also 'typedef' (now that I think of it) statements, it takes that information away from the file in which it's used, which could lead to confusion.

I am just working on small projects at the moment where it won't really cause any issues, but I can imagine that in larger projects with more people working on them it could become a significant issue.

An example follows:

UPDATE: my function prototypes for 'Unit' have string, ostream and StringSet among their return types and parameters - I am not including anything in my header file that is used only in the implementation file.

//Unit.h

#include <string>
#include <ostream>
#include "StringSet.h"

using std::string;
using std::ostream;

class Unit {

public:
    //public members with string, ostream and StringSet
    //in their return values/parameter lists
private:
    //private members
    //unrelated side-question: should private members
    //even be included in the header file?
} ;


//Unit.cpp

#include "Unit.h"

//The following are all redundant from a compiler perspective:
#include <string>
#include <ostream>
#include "StringSet.h"

using std::string;
using std::ostream;

//implementation goes here