Sapiens question: Was the atmosphere & radiation the same for neanderthal man as us?

There are two initial questions that come to mind as I listen to the audiobook Sapiens: A Brief History of Humankind by Yuval Noah Harari:

  1. Was the constitution of the atmosphere different between what Neanderthal man breathed and Homosapiens man breathed?
  2. What about the quantity or variations of radiation on the planet during the time of Neanderthal man?

I ask these two questions because I seem to recall hearing from some documentary that I watched it sometime in the past that the constitution of the air that the dinosaurs breathed was very different from the air that we breathe today. (Maybe it was from one of the commentaries in one of the Jurassic Park videos.) 

That question inspires the question about radiation, because if radiation influences our skin color, then my question is does radiation and also influence the evolution of DNA?

 

(The image provided below illustrates where I am in the book.)