That definitely sounds strange. Did you receive any error message or codes? Any third party plug-ins/devices conflicting with Illustrator?
Can you try the solution outlined here and let us know how it goes? http://helpx.adobe.com/illustrator/kb/illustrator-17-1-crash-imslib.html
As for your After Effects issue, AE CC should work in 10.9.2. How did you find out that it didn't work for your OS?
I am having the same issue after trying to install dreamweaver cc on my laptop and it said I need a newer operating system. So I went back to my pc where all programs worked and now none of the cc programs will open. Please help. I thought I could install the programs on both machines as I want to use my laptop when I go away and my pc when I'm in my office.