There are any backup logs?

I'm using the old backup system with remote backups (via ssh with rsync), there are any backup logs? I want to know how many time takes to do the backup, to calculate the transfer speed between both servers.

Another doubt the backup will be duplicated (in current server and in the remote server) or it will only send to the remote server and erase it on the current one?

you should get email notification of cron if you have set root mail forward