Can I see my actions in automation without stopping the calls?

Yes, on the automations main page, at the right side of the automation created, just beside the turn-on button, you will find a little eye icon, clicking on the eye will take you inside the automation, and you will be able to check the actions configuration but you will not able to edit it. If you want to edit an automation you first have to stop it. However, stoping an automation will stop all current users that were inside the automation.