If I change the prompt after translation in the editing screen, will the text be automatically retranslated with the new prompt.

No, the text will not be automatically re-translated. 

To re-translate the whole document with the new prompt:

・Please create a new translation from the New Document page

・Please select a different engine to re-translate the file 

*If the engine is changed, all the segments translations that were not added to Phrases, will be lost.