I don't know whether she could reverse hom and avsx as she couldn't stop a em pulse from killing her even when she was the Phoenix. maybeee only hope was destined to be the Messiah who could revert hom although come to think of it she had help from the perpetrator in making the spell from hom undone so Jean could have done the same without need of hope.
The pulse killed Jean, not the Phoenix. The Phoenix can't die, not even a "no more Phoenix" can kill it.
Jean likely would have had to fight her dark side. The Phoenix's conversations with Prof X were cryptic.
I could kind of see her shifting more into "survival mode" after M-Day like Scott did, assuming she loses The Phoenix and doesn't just restart the X-Gene.