ADE is supported on Windows 7.
When you try to relaunch ADE after crash, it tries open in the previous state before crash and it will end up in crashing again.
Can you please try below steps:
Take backup of the "My Digital Editions" folder in "C:\Users\<USERNAME>\Documents\" (for Windows) or "\Documents\" (for Mac)
Delete the My Digital Editions folder.
Now add the books one by one from the backup to the newly created folder.
Hope this works