No, Action Comics is a comic book series published by DC Comics. It didn't become DC Comics. DC Comics is a larger publishing company that encompasses many comic series, including Action Comics.
The Comics Code Authority didn't necessarily help comics. It censored content, which could prevent some important and meaningful stories from being told. Also, it might have hindered the industry's growth and innovation.
The Blip is exclusive to the movies. Comics have their own diverse and separate set of events and developments that don't include something like the Blip.
The answer isn't straightforward. Different comics handle the phoenix's fate differently. Some might show a definitive death, but others could introduce plot twists or magical resurrections to keep the character's story going.