Connecting to my wireless volume external HD, there are 2 users listed for it, myself & "everyone". I have read/write access as admin, but "everyone" has "no access", and I can't change this. I'm guessing this is why my volume HD has just decided to not allow me any read/write access to it anymore as I 'don't have the necessary permission', even though no details have changed all week. After admin unlocking to change 'No access', it immediately reverts back to it. Need assistance with how to either remove "everyone", or change that to read/write access permanently.
Try going into Terminal then
sudo chmod 777 /Volumes/ExternalDriveName this should allow everyone access. If it doesn't work, then verify that it is formatted APFS, HFS, FAT32, or EXFAT. If it is formatted as NTFS, then it will be mounted as read only. If it is formatted as something that macOS can write to, then try running First Aid on the external disk. This might fix permissions. Good luck!