How can I increase the size of the dos box to full screen?

It should be as easy as making sure you click in the game screen box and then hit Alt-Enter!

Hope it helps!

Instead of clicking 'Play' on GOG click the icon next to it for settings, then go to Additional Executables > Graphics Settings and launch the game from there. You can change the resolution of the window and add scaling settings (I think 'advmame3x' looks the best with double buffering).