Is it possible to change the permissions for the newly created DSA logs?
May be using any built in configuration file or any other way, so these logs can be utilized by custom scripts where special permissions are required from the application/script side to query them?
The short answer is no.
When the 'DXserver' creates any log file for that particular DSA, it controls the permissions set on those log files. There is no way to alter this from product perspective.