Hi Yslee,
lets have a closer look. The pdf e-book page 3, requirements say the computer used for the exam must be on x32_86 architecture. This is NOT Apple Silicon's ARM. So this one is clear. If Apple, than it has to be on Intel. Apple stopped puting Intel CPUs in their product line in 2020/21. So anything newer is unusable, unfortunately.
Regarding the desktop on i5-13th Gen 13400F. If you look at the specs page, this CPU was introduced in the first quarter of 2023, while the Fedora 37 the remote exam system is based on was introduced in November 2022. So it is natural it is not yet supported. Besides, you use a discrete video card. Many such cards have poor support in Linux distros in general, some work great but need additional drivers that are not always included in standard installation.
Make sure to boot in UEFI mode, perhaps remove the GPU card and run on internal/integrated video, it might help. So you see, the issues you are experiencing with your computers are expected. I suggest you use an older ordinary (not the latest or gaming) computer, you will most likely have no issues. Any 8GB RAM older laptop with integrated Intel graphics shoudl do the job well. No computing power is needed.
Kind regards
