I see you mentioned you talked with the email provider, but is it possible they missed something? Perhaps they changed their outgoing mail server configuration and you have to change it in the mail app. I don't use Samsung Mail, but I would definitely remove the email account and set it up again, or go into the settings and reconfigure the outgoing server. Some email providers (*cough, cough* Google) require third party mail apps to now have a separate one time password. Your provider may have something like that. You can also try configuring and using a different mail app. You can add additional accounts to the Gmail, Outlook, Yahoo, etc. apps.
Well your rmails will move automatically. You are using IMAP which means, unless you chose the option to remove mail from server, they remain in your email account.i don't know why it stopped working all of a sudden, but outgoing mail is defintely a server issue.
