It's there for me when needed, i.e. in menus (main menu, station menus, galaxy map, galnet etc..). In case you mean in the cockpit, there's now way to make it show as far as I'm aware.
Make sure the display on the monitor has the mouse clicked inside the window, then you can move the mouse within the Galaxy map, not sure about in the HUD as I don't use until in there
Yes, this. The window on your monitor has to be active for most things to work. My Voice Attack profile has issues unless it's selected as it's set to use the "Active" window. I do this purposely.