Your old installers do not work. Yes, the ones you saved for when you would need to downgrade purchases to an older OS or re-install on top of a dysfunctional (older) OS. You get an error message. The problem is most likely not with your installer, but that Apple stopped “signing” their installers. Which seems to be an off-line proces…
You can try to set your computer’s date to a date within a year of the OS’s initial release date (while turning off your internet connection) during install or creation of a USB boot stick.
If that does not work, you need to re-download the needed installers. Pay attention to the warnings on this page about carefully marking the various re-downloaded installers, as they will arrive on you computer indistinguishable from each other!
Then follow the download links from below:
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