WordPress.org

Which log is monitored?

Log file path is read from error_log PHP setting, which can be configured by WordPress or otherwise. Additional logs can be monitored by filtering list on error_log_widget_logs hook.

Why so many/few lines?

Filter error_log_widget_lines hook to control how many lines you want to see.

Will everyone see the widget?

Only users with manage_options capability (Administrators) will see the widget. You can change this by filtering error_log_widget_capability hook.