How To Fix “Application Is Damaged, Can’t Be Used To Install MacOS” Failure on older Macs
Please check the following, did you redowload the macOS App? So the certificate issue is solved.

If so you should download the macOS App onto a current Mac Model fresh from AppStore and create a macOS-USB-Stick from the newer Mac, this should solve your issue with the AppStore Authentication, so you will be able to run the installation on your older Mac.