Hello this will help
FTP to your server and go to your data directory and check every subdirectory and make sure it is 777. Also every subdirectory of that has to also be 777. The mini thumbs and medium ones. failed to copy tells me that that specific directory is not 777.
If you have SSH on the new server you can use SSH and type this command
chmod -R 777 /home/name/public_html/gallery/data