Strange problems installing operating systems on old MacBook air? My Questions


Why is the Lubuntu install not working? How can I make it work?
Why are my Windows partitions not showing up in any partition managers?


Confused? Read below.

What I Did


I have an old MacBook air lying around that I had installed Arch Linux on.
I kinda got tired of Arch Linux, and wanted to see the effects, so I did the classic rm -rf / --no-preserve-root.
Yesterday, I wanted to install Lubuntu. I flashed it to a  usb flash drive with Etcher.
I launched the installer and ran it, choosing to erase disk and install Lubuntu.
It was a success, until the end where I got the error grub-efi-amd64-signed failed installation /target/. Looking at the logs, I also got the errors ubiquity: E: Unable to locate package shim-signed and grub-installer: info: calling 'apt-install grub-efi-amd64-signed' failed and the installer crashed.
Thinking it might be a lack of internet connectivity, I connected to ethernet. I know it worked because the option to download updates wasn't greyed out. It still didn't work.
I read somewhere that I might need a EFI system partition, so I manually partitioned it. It still didn't work.
Getting tired of that, I wanted to have some operating system, so I created a bootable Windows 10 installation media with Rufus. It installed perfectly, and Windows worked fine after I installed the BootCamp support drivers, besides no bluetooth or multitouch trackpad support.
Again, I wanted to install Lubuntu, maybe install it to another hard drive (an HGST Touro S). So I opened up the Lubuntu installer again and manually partitioned my hard drive (the external one). Of course, it failed...
BUT I noticed a weird thing. The partition manager in the Lubuntu installer said that my MacBook's hard drive was empty. 100% free space. The same thing appeared on GParted in the Lubuntu live OS.
But that's weird because my computer boots, and on the Windows Disk Management app it says that there are partitions.


Note

I am re-posting a question from superuser that is now deleted. This was recommended here.
I see clear indications you are not thinking through what you are doing. Rather, you are throwing stuff at a wall hoping something sticks.


Normally, I would expect either macOS or OS X is installed. From the operating system, you can determine the model identifier and current firmware version. If necessary, the firmware can be updated by a download or by upgrading the operating system.
The model identifier allows us to determine if the EFI is 32 bit or 64 bit. Whether or not your Mac has a BIOS. If the processors are 32 bit or 64 bit. How to properly download the Windows Support Software. Which versions of Windows will run on your Mac. The type of booting (EFI vs BIOS) available for Linux installations.
You failed to include if you are partitioning using a MBR or GPT scheme. Maybe you are using a Hybrid scheme? Who knows? 
You failed to include which version of Lubuntu you tried to install. From a quick check of Lubuntu's download page, I see there are many versions to choose from. From the information you have posted, I would have no idea which one to choose.


Take your installation of Windows. How did you determine which Boot Camp Support Software to install? Obvious you picked the wrong one, since some of the hardware failed to work. I could not possible tell you how to acquire the Boot Camp Support Software based on the information you posted. I have no idea which version of Windows you choose or if the version was 32 bit or 64 bit.

Where to go from here? Get some version of OS X or macOS installed. Maybe this is the question you should have asked in the first place. For now, an answer to this question will have to wait.