Hi Crystal,
These are very good questions and I hope another scientist can help answer your question as well. But I'll take a first shot.
Yes, the Corona is part of the atmosphere. And solar flares do shoot material from the sun's "surface" into space - some plasma and magnetic fields. I think maybe the confusion is that solar flares are not coronal mass ejections. Scientists are still trying to understand how solar flares and coronal mass ejections are related, so if you decide to study solar physics for a career, you could make some discoveries about these phenomena. Your confusion is due in part because there is still a lot to learn about these two phenomena.
The simplified answer about the difference between Coronal Mass Ejections (CMEs) and solar flares is that CMEs do eject large amounts of mass from the corona whereas most of the "stuff" coming from solar flares is actually light (in different wavelengths, like x-rays). These x-rays come from a region just above the surface, so not quite from the surface proper. But the magnetic fields involved in both CMEs and solar flares are tied to the Sun's surface and these magnetic fields seem to be what make CMEs and solar flares somewhat similar.
Laura