Fixes sql_mode values that cause error:Incorrect datetime value: '0000-00-00 00:00:00' for column 'post_date_gmt' at row 1
No, plugins are not loaded during installation. For alternative solutions see "Other manifestations, alternative solutions" on the plugin home page
No, it uses @@SESSION.sql_mode to change the settings for each WordPress session individually.
Just turn off the plugin - because it uses @@SESSION, the changes wont persist.
If you've made other modifications explained in this plugin's documentation, you will have to run similar SQL commands to apply the old settings.