Looks like you are still having issues with this? Are you absolutely unable to get access to another Mac? If you just want to get this done, and have it work, I would do this:
1) Replace your SATA cable, period. I support a lot of machines of this era and the SATA cables fail routinely and cause a bewildering array of issues. It's cheap and easy to do, so replace it.
2) On another Mac, assuming you have at least one usable 16GB USB thumb drive as well, download OCLP (OpenCore Legacy Patcher).
3) Using OCLP decide which OS you want to run and build that installer. Don't forget to install OCLP to the EFI partition of the USB thumb drive. (Be sure to choose the TARGET model, otherwise OLCP will assume you wish to build an installer for the model it is currently running on.)
4) Boot from the USB Thumb drive you created. Erase the internal SSD and install the OS.
5) Boot from the internal SSD and wade through an initial account setup (will be very slow with the UI responses, but absolutely doable)
6) Install any OLCP Root Patches and Install OCLP itself to the EFI partition of the internal SSD
7) You are basically done, and now have a Mac running a recent OS.
I support a LOT of old Macs and in all fairness using OLCP is now faster and easier than wading through Apple's own obtuse reinstall processes. Research it a little first, but if you just want to get this system running with a minimum of fuss so you can hand it to your nephew, this is the way I would do it.