Hi there, it seems that the automatic Mac restart makes your FAT hard drive function abnormally. Incidentally, you'd better use a self-powered drive which has a lower coincidence of drive failure. As for the error you received, it's because Mac supports the FAT files system partially so Disk Utility cannot fix a FAT hard drive. You can borrow a Windows computer to perform the disk repair.
Before the repair, you should fetch all files and folders on the drive first. Since you cannot access the drive, iBoysoft Data Recovery Software comes to help. It can scan an inaccessible, unreadable, corrupted, and broken internal/external hard drive for lost files.
After you have all the files at hand, you can then use Disk Management to fix the external hard drive. If you aim to use this drive on Mac, you'd better format the drive to a file system compatible with Mac, like HFS, HFS+, and APFS.
