ISSUE:
When you attempt to restore a MySQL database from a previous backup using phpMyAdmin, the restore fails with the following error:

Can't create database 'database_name1'; database exists

CAUSE:
This is because the database already exists, because it was created in PLESK.  PLESK doesn't alter the phpMyAdmin SQL Dump script to remove the CREATE DATABASE `database_name1`; clause.  Therefore , when you execute the .sql file in phpMyAdmin to perform a restore the database already exists and phpMyAdmin halts execution.

RESOLUTION:
Simply edit the .sql file and remove the line that has:
CREATE DATABASE `database_name1`;  where database_name1 is the name of your MySQL Database.

Then execute the .sql file in phpMyAdmin for the restore function.