I have seen the error message regarding a "missing firmware partition" while installing macOS 10.13+ whenever the internal drive is missing or improperly formatted. I have never seen this error when installing any older versions of macOS since only macOS 10.13+ includes a system firmware updater within the macOS installers.
Have you tried running the Apple Diagnostics to see if any hardware issues are detected? Unfortunately the diagnostics don't detect all types of drive failures. I can provide instructions for creating and using a bootable Linux USB stick to check the health of the internal drive if you are interested. There is also a possibility that the hard drive SATA Cable is bad which is very common with the 13" non-Retina model.
If you are trying to install an older version of macOS 10.7 to 10.12, then you will need to properly erase or partition & format the whole physical drive (depends on which OS you are installing). If installing macOS 10.11 or 10.12, then select the physical drive and erase the physical drive as GUID partition and MacOS Extended (Journaled). If you are installing macOS 10.7 to 10.10, then partition & format the physical drive using the instructions in this article:
https://www.owcdigital.com/assets/support/support-formatting-and-migration/Mac_Formatting_6-10.pdf