Answer: Yes to both questions.
Hazel.log 3.2 MB
Hazel.prev.log 5.05 GB
Double-click on Hazel.log, opened the log in the Console.
Closed Console App, opened Hazel, clicked Help >View Log and Hazel.log opened in Console.
Closed Console App, closed Hazel, clicked Hazel on the menu bar and Hazel.log opened in Console.
Everything is normal now.