Use the highest resolution, It always works best for me because it's a pain in the hassle hoff just to not see my other utilities when playing.
I've tried it, it attempts to display on my laptop anyways but it gets weird lines and stuff
Is there a way to set the tv as the primary monitor? If so try that
Right click on your desktop and go to "Screen Resolution" and see if there's something like "Show both desktop 1 and 2" or try only showing Desktop 2 and see if that works.
Try putting it into Fullscreen on screen 1, and then pressing Windows Key + Shift + Right to move it to the second screen.