How does ManageWP sends command to backup and upload backup to external destination? Do you use specific ports for this?

ManageWP sends the backup command over a standard web port (port 80 or 443). Port used to upload the backup file depends on the destination, and it is a standard web port for most of the services.
If FTP is being used, then the usual FTP port is utilized (port 21) and for SFTP – port 22.