Issues: CentOS 7.x server running an instance of cPanel / WHM. There is an issue with the UI that interferes with import and export of databases, particularly when they are several megabytes in size. Using the UI, import, export is painfully slow.
Solution: Access SSH, and use mysqldump to move databases.
To export one specific table (for example):
mysqldump -u database_user -p database_name table_name > file_name.sql
If you are accessing as root, each database dump file will reside in the root directory.
Naturally, enter the database user password (for that specific database) when prompted.
To export the whole database:
mysqldump -u database_user -p database_name > file_name.sql
To import the whole database:
mysql -u database_user -p database_name < file_name.sql