Answer to Question 1
The expansion of the Big Bang cooled the temperature to below 100 million K by the time the helium abundances could have allowed carbon production to start.
Answer to Question 2
Quasars vary over a period of weeks in brightness, and vary a great deal in luminosity from object to object. We need a uniform, consistent standard candle, and the run-away detonation of a 1.4 solar mass white dwarf in a Type I supernova gives us just the desired combination of luminosity and consistency.