I want to upload my new site and replace the old one. Will Xara delete all the files from the old site and install the new, or will I have to do the deleting manually?
. . . . Do you know if Designer Pro is designed to delete the old site files though . . . .
AFAIK Web Designer can only replace what it knows exists automatically, ie if the old site was created in another program then it cannot 'delete' the old version.
Web Designer does have the capability of Exploring the webspace, just as you would with FileZilla.
Website Properties > Publish tabbed section, Other host (FTP) and click Explore Web Space, note your site ftp details are required for this. You will get a standard explorer/ftp style window showing all the files that are currently on the server.
In both cases you still have to delete the site manually.