Please check the video tutorial to see how to save the translation file correctly. You can remove the plugin and translations would remain. Also, translations would remain after each theme update.
In order to translate the WooCommerce strings, you need to create a separate translation in Loco > Plugins > WooCommerce in the same way as shown in the video.
In addition check the Theme Settings > Login/Register and Woocommerce > Settings > Account and Privacy/Advanced.