MacbookPro mid 2012 reinstalling OS not possible

the disk you selected in every screenshot, that contain MacOS Base System and has a size of just over 1 GB, is the Recovery software. That disk image is pulled out of the Mac's Read-only memory, and the disk image is Mounted to run Recovery. MacOS Base system Is Never the destination for installing on.

The only other device showing in disk Utility appears to be a DVD reader.

A drive that will not tell Disk Utility is make&model and a reasonable non-zero size/capacity can not be repaired or mounted to be used for any purpose. That drive has died.

Additional forward progress will require a replacement drive.

Is this the Retina or non-Retina model?

If it is the Retina model......was the internal SSD replaced/upgraded with a third party internal SSD? If so, then you need to boot into a macOS 10.13+ installer before a third party internal SSD can be seen.

Otherwise, @Grant is correct that the internal drive has most likely failed, although it is also possible the internal hard drive SATA Cable could be bad especially if it is the 13" non-Retina model.

Assuming there is no accidental liquid damage, then the SSD or the SATA Cable are the most likely suspects. Remove the SSD and connect it externally using a USB to SATA Adapter, drive dock, or enclosure. If you can boot or see the physical SSD, then the issue is most likely the SATA Cable or possibly the Logic Board.

If you still don't see the physical SSD when connected externally, then the SSD has most likely failed. The SSD completely disappearing from the bus is the most common type of SSD failure.