You can use the F7 key in a cmd.exe session. The more braindead command.exe sessions, however, don't support F7 for command history. The doskey utility should provide command history for you even in command.exe sessions, but I'm not sure if it works with current versions of command.exe (I seem to remember Microsoft broke some stuff).
I don't know, off the top of my head, where MS Windows stores cmd.exe session history.
I'm not sure what you mean by "Run Box". I usually hear that term in reference to the "Run" dialog that you can bring up from the Start menu -- which doesn't really have anything to do with cmd.exe session history, as far as I'm aware.