Is it possible to save the statements run on the Editor along with the output?
Yes that is possible.
To do that please follow the steps below:
1] Type "set echo on' in the Editor.
2] Type the statements you want to run.
3] Run F5.
4] Go to the Script Output tab in the Script Output window: Your statements will be recorded along with the output just like SQL*Plus.
5] Then you can choose to output to a file from the output menu (r-click |Save to File).