Vanilla Pudding: Could someone explain this recipe to me?
I don't know why this pudding is especially &quot;easy&quot; -- it's similar to other pudding I've made. Perhaps I've always taken the easy road...

Salt is a flavor enhancer that makes nearly everything taste better (e.g., enhance sweetness, reduce perception of bitterness. There are many more links on that topic; that was the first reasonable one I saw.) I don't think salt is magical in any other way in this recipe.
Adding ingredients after cooking: For vanilla, it loses some of its volatile taste/aroma when cooked. Common to add vanilla and ilk near the end of stuff like this (and sugarwork, other cooked confections, etc.).
Sieve: For smoothness. To get out the lumps. Sometimes done for certain things like crème pât, and sauces or gravies. In this case, to ensure that no starch (etc.) lumps remain. Another question/answer suggests to use a blender (e.g., immersion blender) as a possibility also.