Ah, parents! Never understood them until my wife and I made them grandparents! I will be surprised if they go by a random person on an online forum, but we'll see.
To answer your questions:
1. I am not sure where you are, but a replacement drive similar to what you had is around $50 USD.
http://www.newegg.com/Product/Produc...98&ignorebbr=1
1a. If you have particularly understanding parents, you can ask them if you can get a solid state drive for the laptop, and this particular issue would never happen again
http://www.newegg.com/Product/Produc...82E16820148820
as these drives have no moving parts.
2. The reason I say discs plural is because all or the restore data probably will not fit on one disc. The original restore data that came on the computer is sitting on the hard drive that is dying.
3. To order restore discs for you laptop, this page will tell you what to do:
https://us.en.kb.sony.com/app/answers/detail/a_id/40648/c/65,66/p/48903,49902,55369,55424/
4. Hard drives die for various reasons, and to be honest it is amazing they last as long as they do. In your case, you have a disc that is spinning at 5400 RPM (desktop drives spin at 7200 RPM) whenever the computer is running, with nothing but a few mm between it and an arm that moves to grab the data that the RAM is requesting, based on what you are asking it to do.
5. If you don't care about recovering data on the drive, I wouldn't worry about the enclosure.
Good luck!