edit: removed the first part, its been covered
in regards to permissions you set the host path to be owned by the PUID/PGID of the account you are using across all your “media” containers and give it full rights to that folder and all subfolders. if you do that then you shouldnt have any access issues at all, and you shouldnt need sonarr to change permissions.
if youre using different PUIDs for each container then make sure all of them are in the PGID group so they have full control
you may want to use this command to connect to the container and check the volume mappings exist, the path is there, and that you have access;
docker exec -it YOUR_CONTAINER_NAME_GOES_HERE bash