Hi,
the replication errors are not related to your problem.
The fact, that you have only this small number of entries in the /system/console/slinglog screen (only 1 logger and 1 appender) is interesting, because a default AEM comes with some more entries (it writes a request.log, an access.log, update.log etc). So either you have messed with the default configuration (I would never remove loggers, but only add new ones) or the system you are working is in a way broken.
The exception "org.osgi.service.cm.ConfigurationException: oauth.config.id : Config Id must be unique" shows me that you have played with this instance quite a bit, so maybe rebuilding it from scratch is much faster than diagnosing strange issues which arose out of experiments with AEM.
Jörg