your RADIUS should log all connections and sessions
what connections do you mean? establishement of the session, or TCP connections?
you may use NetFlow (IP → Traffic Flow)
hmmm… you may send to syslog firewall rule with connection-state=new, action=log, but it’s only the beginning of connection, without time and traffic info
use mangle, not nat
to write logs to different files - read your syslog daemon documentation, something about regexp filtering, and add log-prefix to mangle rule