For Databases
Create the database inside Plesk under the proper domain. Make sure you set the same database name , database user and password. This is really important.
After that copy all files from /mnt/old_drive/var/lib/mysql/database/ to /var/lib/mysql/database/ where database is the name of the database you copy.
cp -R /mnt/old_drive/var/lib/mysql/database/* /var/lib/mysql/database/
After you are done with copying all database you need (be sure you copy only the ones for your websites. Databases like psa, phpmyadmin*, mysql, horde etc, are NOT to be copied ) to fix permissions again. Run this command in ssh terminal with root privileges:
chown -R mysql:mysql /var/lib/mysql/database/*