This is a really common issue in a lot of non-FPS/TPS games, and is less of an issue here since it's turn based (so you won't accidentally hit outside in haste), but it would still be nice to lock the mouse to the main screen/application, especially in fullscreen mode.

There is 3rd-party software like Ultramon (shareware) that lets you bind a key to lock the mouse to the current window.  It was a little clunky the last time I used it (~a year ago), but it's nice for apps that don't support dual monitors (i.e. apps that don't know to lock the mouse to the app in full screen mode).  I think there's free software that does something similar.

The second thing you're looking for (extending the app screen to show the map on one monitor and pieces of the UI in another) is a different feature and something I've only seen in WoW.  Really nice, but not widely supported.