How do i find a supercritical airfoil for my preliminary design?
Answer to the implicit question: Yes, the more recent airliner airfoils are indeed secret. Look for reports like this to see what is out there.
Answer to question 1: Try the linked NASA Technical Paper 2969.
Answer to question 2: Your viscosity is for sea level. Try to use the value for the tropopause and it will be only ⅓ as large.