Is there a way to edit multiple Jabref entries? E.g. add the same data to an empty field, like "keywords", of multiple files?
Yes, there is. Select the entries you want to edit, then choose "Tools">"Set/clear fields" in the menu bar. This will bring up a dialog prompting what field and what value (also with a "clear" option). There's also a checkbox allowing you to set only the empty field to a certain value.