Both. Couple examples: several disk image files that I created 10+ years ago, and have stored on the same computer except for short periods when the operating system was reloaded and they were transferred to an external drive. They still work fine and I can mount them as images, however, blank page icon. Other disk image files work fine and still have their proper icon. (These are stored on a Beige G3 running 9.2.2.)
Another one: I had a floppy disk that contained a Word document that I created years ago. It had the proper Word icon when it was on the floppy, but when I copied it to the desktop on my LC630, the duplicate file now has a blank page icon after rebooting the computer. Still opens in Word and does not appear to have been corrupted.
I am not renaming any of these files, if they actually had a DOS file extension, I left it alone. Although most of this stuff I am having a problem with does not have one.
FWIW, I can open Word (for example) and create a new document, save it, and that new file will have the proper icon.
Not that I can recall, however, my system 7 usage is so infrequent these days that I can't say for sure.
No, if the machine in question has a network card, it's connected to the same network as everything else, and generally they will connect to ONE share on my Beige G3.