Wondering what the real end date is for Muse, and right now I am unable to download my current site to rebuild in another program.
#1 The end date is irrelevant because Muse software will keep working beyond March 2020. But the sites you created with it might not work as well as they should. Given that Muse is no longer being developed, you should find another web authoring tool to use.
#2 To get site files from your web server, use a dedicated FTP client like Filezilla (it's free).
Have you got fees outstanding with your hosting service?
As Nancy points out, this doesn't sound like a Muse issue