Does your CPU has integrated graphics? You can remove your GPU and then you test if the error still occurs to find out if your GPU has damage. You can also test a live system, to exclude issues in your OS or driver configuration

Which OS and GPU do you have in use?

You can run Memtest, just boot it and check the ram. Some Linux distros have memtest included in their bootable image (e.g. Ubuntu). Otherwise you can create a bootable stick with memtest by yourself.

I experienced some bugs while gaming on Wayland even with an amd card. My workaround was switching back to X11 for gaming. That said, I didn't even notice that I was using Wayland by default for a long time until Firefox completely switched to Wayland I experienced some heavy artifacts in Firefox (only if it's full screen on my second monitor, but that's a daily thing). And because of that, switching back to X11 isn't a workaround anymore, unfortunately its my new default.

That's it. I have installed Ubuntu many times connected over Wi-Fi without any problems, except one special case many years ago. In that case, the system had some brand new Wi-Fi adapter, so I had to install the driver over Ethernet. But in almost any case it just should work and you can simply try to get a wireless connection in a live sytem to find out. And as mentioned above, internet connection is not necessary while installing from USB stick with the usual image. Its just recommended to save time and install the latest updates of some components during the initial system installation. But of course, you can do it later and of course you can do it over Wi-Fi (except some very rare special cases as mentioned at the beginning).

Just to avoid any misunderstandings for the furture: you can run NVIDIA cards in ubuntu, you just have to install their proprietary driver. And on ubuntu, its pretty easy to do so. I used a few different nvidia cards on Ubuntu in the last years and never experienced any issues after installing the recommended driver. Before installing the driver, I got some flickering and artifacts, but with the right driver everything should be fine. And even for amd graphics you can install the proprietary drivers from their website to get out the maximum performance of the GPU. But for amd you can also use the "pre-installed" open-source driver, which has a much better performance in comparison to the open source driver for nvidia cards. Integrated grahipcs are supported out of the box in almost any cases.