Hi,
1, Based on my research, Audit logs will not get sync between all the DCs. DCs just log the events for themself.
2, For send audit logs to system log, you can refer to the following link: https://social.technet.microsoft.com/Forums/ie/en-US/66587a55-2883-4365-be7d-ab5baed50dc0/need-to-collect-security-logs-from-all-domain-controller-to-central-location?forum=winserverDS
Best Regards,