Do I need to click a save button when editing a form?

No. When you edit an existing form, changes are saved automatically about 1.5 seconds after your last edit. The editor shows "Saving…" and then "Last saved" with a timestamp. If the form is in an invalid state (for example a missing name or group), it stays unsaved and inline errors are shown until you fix it. Only brand-new forms have an explicit "Create widget" button.