Yes, the generator comes with a 5m cable to connect the Delta 2 and charge it with direct current. You can set thresholds via the app from when and how much to charge.

DC charging is also possible, but you need an additional cable: https://youtu.be/YB7_jfewx4...
The video gives quite good information.

Yes, but only AC charging, DC charging including the smart functions is only possible with Delta Pro or Max or their additional batteries.