I want to download my emails to eM so that they are removed from my mail-hosts server, how do I do that?

To do this, you will have to set up the account again, this time as a POP3 account.  POP3 simply downloads emails, while IMAP synchronizes with the server.

To do this, instead of doing an automatic setup, chose mail and then other.  Enter the server information (generally available for the email provider website).  Also, make sure you deselect the option to leave emails on the server.