They come in PATA and SATA style, you need to know which type of drive is in the laptop. The caddy that you linked to goes in a CD/DVD bay, and requires the computer be working (obviously, I hope). The external enclosure allows you to hook the hard drive to any computer that has a USB port. Short version, you won't lose any files just because you lose the motherboard.
I don’t think so. “laptop hard drive enclosure” on Amazon or Ebay, and find one that fits the drives you have in there. Good Luck.