Without more specific details nobody can tell you much, but perhaps you might want to spend some time on your Radeon control panel. It seems to me that you might need to spend some time and disable some features to "dumb things down" like turning off some OpenGL extensions or setting the level lower (in case of AE CS6, OGL 2.1 would suffice). Same might apply to your otehr crashes. Current Radeon models even have specific acceleration features for 2D window drawing and the like, which may not go down wel lwith legacy versions of programs...
Did you ever solve this issue? Please let us know the details so that we know you're OK and for the education of others.
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Yes. I found out that the problem was not related to After Effects. I tried downloading my AMD graphics card driver as I saw it wasn't there and everything started working normally.
Thank you for following up!