Is analogWrite() not affected by blocking codes and/or Interrupts?
is the analogWrite() function 
  continue generating near-consistent PWM when it encounters blocking
  codes or signal interrupts?


Yes for 'hardware' PWM used by analogWrite on AVR and SAMD Arduinos. The hardware PWM is handled by wave output of Timers, which are MCU peripherals running independently from CPU and other MCU peripherals.


  Is it the same case for both the classic arduinos(atmega chips) and
  the new arduinos(SAMD21 chips).


yes


  If analogWrite() does get affected by blocking codes, is there a way
  to create a uninterruptible PWM signal?


N/A