We are told the Shechina is on us when we learn Torah.Does this apply to any Torah and to what degree? Does it apply if I pick up a book written by a Rabbi as well if I pick up the Talmud? And is the degree of Shechina different or the same, depending on what you are learning?

The Mishna which you are referring to (Avot 3, 6) differentiates between the number of students, but doesn't differentiate concerning which Torah material is being studied. In addition, one of the verses (Tehilim 82, 1 ) cited there twice as a proof, relates to a Jewish court, which deals with the Talmud and Oral Law, which includes books and Torah of latter day rabbis, as well. Accordingly, clearly any Torah study upon which we say Birchot HaTorah is clearly included, whether the Written or Oral Torah, which are both Godly & necessary.