Can't boot from eMMC, only from usb

I managed to install linux on my lenovo 100e 3rd Gen, the problem is that it won’t boot without the media USB, meaning I can only use the live linux. Is there a way to bypass that? I can access a live version of Fedora, and it actually install as it should, but the UEFI does not recognize the eMMC drive. Is it possible to do anything at all? or do I always need to carry a usb stick with me?

You can install to internal storage, but you will still need to put /boot/efi and /boot on removable storage. The difference between that and running a live environment is you can unplug the USB after booting I think.

I have been having a similar problem, except when I attempt to install any distribution of linux, some progress is made and then the installer freezes. Not sure if this is a related issue or maybe my problem warrants a separate thread?

Start a new thread. You have a entirely different problem.

If you are running linux only, you need repartition the emmc drive. Most live distros have gparted. You have to create a gpt partion sceme to boot on most systems first. Most installs use a small (250 meg) EFI for the type format to Fat 32. Then add a
primary partition format as ext4. You boot image will be installed on that EFI partition and will allow you to boot from the emmc drive. If you have trouble, hit escape at boot, go to bootmanager boot from file, and choose you kernel image.