Since the last update of both server connect and extension manager, every time I save an Action Step I get a message that 'Parser.php' will be updated with a dialogue box. It resides in: dmxConnectLib\lib\core\Parser.php.

Hello Arnold,
It is normal to see this message once, after you updated the extension. The file gets uploaded and overwrites the existing one on your server.
Can you please compare the dates of the two files:

C:\Users\username\AppData\Roaming\Adobe\Dreamweaver CC 2017\en_US\Configuration\Shared\DMXzone\dmxServerConnect\Includes\PHP\lib\core\Parser.php

and the one in your site folder:

dmxConnectLib\lib\core\Parser.php

If the issue persists - please remove the whole dmxConnectLib folder locally and on your server and save the action file. This will put the latest files on your server.

Please open DMXzone Extension Manager and re-install DMXzone Server Connect. The issue has been fixed.