“using namespace” in c++ headers

In all our c++ courses, all the teachers always put using namespace std; right after the #includes in their .h files. This seems to me to be dangerous since then by including that header in another program I will get the namespace imported into my program, maybe without realizing, intending or wanting it (header inclusion can be very deeply nested).

So my question is double: Am I right that using namespace should not be used in header files, and/or is there some way to undo it, something like:

//header.h
using namespace std {
.
.
.
}

One more question along the same lines: Should a header file #include all the headers that it's corresponding .cpp file needs, only those that are needed for the header definitions and let the .cpp file #include the rest, or none and declare everything it needs as extern?
The reasoning behind the question is the same as above: I don't want surprises when including .h files.

Also, if I am right, is this a common mistake? I mean in real-world programming and in "real" projects out there.

Thank you.