Illustrator saves, but gives message that it hasn't saved, asterisk remains near file name.

To be safe, I would save as and for example add a 2 to the end of the filename. The file might be locked, or some confusion over this cloud version local version. I would also turn off pdf compatible unless you absolutely need. Important to know if this is a false error about the asterisk, so please get back to us and we can help you better, after saving version 2 as a safety net.

After file is safely saved, you can restart your computer system, not sure what you are running, to clear up anything in cache which migth be conflicting. If this returns we will show you how to reset the OOBE.