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The edit screen keeps saying that the file does not exist or the directory is not writeable even after I click save.

Check the permissions on the plugin directory comicpress-companion/custom - For more information on this, contact your Webhost. If you are running WPMU make sure that the blogs.dir for the current blog's /files directory has the proper permissions as well (again as your webhost).

I'm having another problem.

If it's a serious problem, such as WordPress becoming non-functional or blank screens/errors after you perform certain operations, you will be asked to provide error logs for your server. If you don't know how to get access to these, talk with your Webhost. At that time just remove the plugin from the plugins/ directory. If it still continue's it is probably not a ComicPress Companion problem.