Should I rebuilt my partition tables using the files you uploaded?
You can try. This are 'Max filesystems and kernel.
Are there files for sda6, sda9, sda10?
sda6 is provided (this is the kernel), and sda9 and 10 not. These don't contain any data. Sda9 is only an empty filesystem, and sda10 is completely blank.
The 2Big2 instructions tell how to treat this.
my MAC logs
What are MAC logs?
Command sent : bootm
bootm is the command used in u-boot to boot the (uploaded) kernel. This kernel then downloads the capsule over tftp, which apparently happens. 'Apparition' is french for appearance. Lacie is french, so I suppose someone forgot to translate this. And I also suppose this means the software waits for the NAS to reboot and become available.
The capsule is transferred over tftp, which doesn't have any error detection and recovery. So the capsule might be crippled during transfer.