Driver issue on diskless windows installations

[NiKiZe]

You need the correct driver package. The invalid certificate after reboot is due to the wrong package being used.
You not only need the .sys file but also .inf and .cat, and you need it for the correct OS
If you take the files from Windows 10, it might be that it is not "supported" in windows 7.

During the first PE step these things are not checked.
What you need is the same version of PE as the actual version you are installing, and then you need to add (install at runtime should work fine) the correct driver into PE which it should then copy over during installation.

You should be able to find the correct files in any of the "intel network drivers" that you can download from their homepage, just extract their setup program with 7zip or similar.