How To Easiest Do Backup And Transfer Of Mysql Files

I have following problem-i have over 20 sites on server and each site has own database.Is there a way to speed up backup and transfer or other server?

Method which i use right now it's following:first i archive entire directory using command tar -pczf name.tar.gz public_html,and then repeat with each directory.But i think i could simply archive all requied directories,but that will took toomuch time,so if i drop connection during archiving it wont be archived at all then.So i think best solution will be to create some kind of batch command which can load in background,so that means command wont stop if client lost connection.

So let's say i have 2 sites and two directories located and different places.

One is at home/site1 and other at home/site2
So i think i would need to put command into batch file
tar -pczf site.tar.gz. /home/site1 and tar -pczf site2.tar.gz /home/site2

Will that work? Also second part,mysql databases,i founded if i login into phpmyadmin as root i can see all databases.I managed to export all databases,but question will import again to phpmyadmin work.I think phpmyadmin create command for each database "if there is no db sitename_mysqlbase,create it",but howmuch i know phpmyadmin have limit with importing size of mysql database.Could that be done with import/export mysql command?