@MCS2014
I'm not sure why you are getting the Keychain window. But it is asking for your Mac user password, and you can select "Always Allow" as sawinglogz suggested. It might be something Apple changed with Big Sur, or just that KeyChain has always been a littly quirky.
The first screenshot of terminal you posted (with the keychain one) doesn't show rsync copying anything. Just that it compared files from its list. Are you trying to copy files more than once, or running the app numerous times? rsync will only copy files that have changed since the last time it ran, which should be the 6 or 7 files from the previous night. So if you run it a second (or third) time the same day it won't necessarily have anything to copy.
From your second post...
It almost seems like you have FlashAir mounted twice "Unmount failed for 192.168.0.250 (1)", the one in the parenthesis usually means it's a duplicate. Which is rather strange for a network connection. If you open Finder and look in the left panel, do you see your FlashAir still mounted? Or mounted twice?
Post a screenshot of Finder when you get the Unmount Failed error.
Also open Terminal and copy/paste the following command which will show what is mounted in /Volumes
Have you ever had Finder open while the script was running and clicked on the FlashAir folder? That might cause the unmount to fail because it will show Finder busy using it and refuse to unmount it.
For the Unsecure Connection....that is expected. The FlashAir card only supports http so it's just your OS informing you. Nothing can be done about that. You should only see that the very first time you ran the app. But it's all in your private (internal) network and nothing anyone from the internet can see.
Are you still having issues with your ISP equipment? Or did they replace the modem/router yet?