Views Data Export - Selectable fields Is it possible to select fields for the export?

For example: When i click button it shows me a popup, where i can select content i want to attach to the exported file.
Currently this is not possible. You can always build a view that contain only fields you need. Or select fields when configuring view's display.

Developers needed to choose between GUI on export and unattended processing. They choose automation capabilities, and for good reasons - large exports can take a long time, so it makes sense to trigger them at night using drush.

If you believe there should be such option, then you can fork project - it's opensource, GPL v2, so you have full right to do so. You can also file a feature request in module's issue queue, but personally I don't think it would be implemented by maintainers. If you will provide ready to use patches, then maybe.