Is ranked and "normal" (quick play) MMR separate?
Solution 1:
Yes.
This became abundantly clear if you played QuickPlay in the off season between Competitive seasons 1 and 2 and again between seasons 2 and 3.
Why? Because people who played exclusively Competitive were queuing with the same QuickPlay MMR they had before they switched over to playing Competitive, meaning that they were often being matched against teams whose players were considerably worse at the game.