"My question is, if that device were to die, but leave the hard drives in good shape, could the hard drives be moved to a new buffalo device or anything supporting sata drives and the data would still be accessible?"
Possibly, but we do not support it. This unit was never meant to be disassembled.
"What if only one of the drives worked, could it still be moved out of it's RAID1 setup to anything supporting sata and the data be accessible?"
You can hook the drives up to a linux machine or use software programs that specialize in RAID recovery (like UFS explorer). Once again this is not supported and will void your warranty, but if the data is more important then it is always an option.
The best way to protect against data loss is to have a good backup plan. If you have up to date backups then you have nothing to worry about. Just use a USB HDD to back it up from time to time.