LunaSea currently offers a free cloud account that can be used for extending the functionality of LunaSea. The only details required to register for an account are an email address and password. At no point will LunaSea or the developers send you any emails, unless you explicitly request a password reset email.
The three options related to backing up your encrypted backups should be self-explanatory. All configurations are encrypted on-device before being sent off the device. When restoring an encrypted backup, the encrypted backup is downloaded to the device and you will be prompted to decrypt the backup on-device.
Deleting a backup is a permanent action, there is no way to restore that backup.