1) If both servers are online, then you can copy them with scp. Example:
scp www.tar.gz firstname.lastname@example.org
(Why backup /etc? If you restore on a new server you will get problems?)
You should not restore it on the new server. You just backup it in case that you need any of the config details and to have the /etc/passwd, shadow, group and gshadow files at hand for step 5).
2) Backup only the client databases and dbispconfig database. The command you posted will backup all databases to one file so you get the problem that the mysql.mysql database is included but it should not be restored on the new server. You might be able to add a exclude statement if you dont o´want to backup databases one by one.
a mysql dump can be imported with:
mysql -u root -p < backup.sql