For the parsnips:  Peel, cut into bite-sized pieces, and boil until soft.   Then put in a blender with some cream, unsalted butter, salt, and pepper.   When creamy, they are ready. Unlike mashed potatoes, these will not get gummy if done in the blender.  

For the duck, slash the fat and cook over medium heat, fat side down, until most of the fat is rendered out and the remaining is crispy and brown.   Flip and continue to took until mediun rare (or medium if you insist).   Use an instant read thermometer!

For the gastrique, use this recipe: https://www.seriouseats.com/crispy-duck-with-blackberry-gastrique-recipe