What is the ruling on introducing friends to websites that contain both permissible and impermissible matters, and is it considered a double-edged sword, or is it forbidden to give them access to such sites?

It is not permissible to direct people to websites containing forbidden content if it is highly probable that the person being directed will use them to view forbidden things. Instead, one should direct them to websites that are religiously sound. The general principle is that things that can be used for both permissible and forbidden purposes are allowed, unless it is highly probable or known that they will be used for forbidden purposes.