On most-all terminals, you can print the ASCII carriage return '\r' (value 13 decimal) to return the cursor to the left of the current line, allowing you to overwrite the previous value. Or, you can send backspaces ('\b', ASCII 8) to move a single character left. Neither will automatically remove content already displayed, but you can always overwrite anything you no longer want to see with some spaces. Alternatively, you can use control codes supported by your particular console (e.g. vt100, vt220...), which will probably have more advanced features such as "clear-to-end-of-line". Many libraries are available to detect the terminal type and use codes it supports, or synthesize advanced operations from many simpler ones where necessary: on Linux and UNIX, the ncurses library is a good choice.
C++ has no concept of console windows. Opening a second window depends a lot on the operating system you're using, and perhaps the graphics library, neither of which you specified. On any OS though, you can have your application write some messages into a file, then inspect that file from another window that you open yourself. On Linux/UNIX, the utility "less" is great for inspecting log files - as well as showing you the contents at the time you ran less, you can ask it to "follow" new data as it is written into the file.