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Any other function I could use?

Yes you might want to use the conditional function is_authenticated() function. It requires one parameter, a user ID, it will return TRUE or FALSE

Will it create any new database tables?

No, it doesnt create any new tables. The Plugin just adds a usermeta value 0/1

Is there any language file?

Not yet, I hope to add one in the next version.

I can't activate the plugin in WP-Backend. What should I do?

Sometimes there is bug that the plugin won't work if the confirm-user-registration.php is in a subfolder in WP-Plugins. Try to put the file in ./wp-plugins/ instead of ./wp-plugins/confirm-user-registration/