Python Logging (function name, file name, line number) using a single file

I am trying to learn how an application works. And for this I am inserting debug commands as the first line of each function’s body with the goal of logging the function’s name as well as the line number (within the code) where I send a message to the log output. Finally, since this application comprises of many files, I want to create a single log file so that I can better understand the control flow of the application.

How do I log plugin (cron) actions?

Is there a recommended way to log (failed) cron actions from your plugin? For example, I have a plugin that synchronizes with an external service every hour. I want to log how much was changed, but also when the synchronization failed. What would you recommend here? A new database table? The Log Deprecated Notices plugin does this with a custom post type, but this might be too much overhead? I believe WordPress does not come with a standard logging package?