Hey Christina,
Is the filter that you're unable to edit or remove:
Member of Engagement Program
Member of Engagement Program is any
Program is 'Engagement Program Name"
Stream is not "Current stream that you're editing"
If so, this filter is required and just says that someone can be pulled in if they're in the current engagement program, but not in that stream. The related flow step just says to pull them into the stream. You can add additional filters or flow steps, but those two are required for the transition to occur.
As far as the edit > close without saving, it sounds like that might be a bug as it should auto-save. I'd reach out to support.