Where can we find the Replication agent status log on the File System? The log can be opened from GUI by using the "View log" link on the agent page.
There is no such log on the filesystem by default. What you can see by opening "View log" link is only the last XX entries which are kept in memory.
However you can configure your own loggers to keep track of replication agent activities in the file.
Check documentation http://dev.day.com/docs/en/cq/current/deploying/configure_logging.html how to create own loggers.
You need to use com.day.cq.replication.Agent.<agent> as logger name, where <agent> is a replication agent name,
eg. try com.day.cq.replication.Agent.publish to create logger for Default Agent (publish)