Yes, she did. Her writing might have been inspired by her life with Dr. Seuss, sharing some of the same whimsical and imaginative elements that his works are famous for. Maybe her stories were read and loved by a smaller audience, but they still added to the overall body of literature associated with the Seuss family.
No. Dr. Seuss was a very creative individual who wrote his own stories. His unique style and imaginative worlds were his own creations. His wife did not write the stories that are so famous and beloved around the world.