If I select files to backup to both Cold Storage and Instant (Hot) Storage, will it be backed up twice?

No, the selected files will not be backed up twice. The priority will always be for the Instant (Hot) Storage.

If you wish to store the data on Cold Storage, please remove the selections from the Smart Selection and the My Computer tabs, and only select them under the Cold Storage tab in the Zoolz/BigMIND client installed on your computer.