Hi. I am not related to Tauon team, but I can share some thoughts.
1. Yes, PC-1 can boot linux from SD card.
2. SoC is Allwinner H3. It is stated on the box actually. If you are mad enough, you can try to run SD card images released for other H3 boards e.g. Orange PI One.
3. I strongly suggest to get good fast SD card before trying anything. Really. SD card is a bottleneck.
4. There are three major ways to use desktop linux distributions on PC-1:
4.1. chroot / android. You will need some X11 or wayland server for android and also some solution for sound output. You can try Xorg with fbdev (framebuffer driver) or something like this:
forum.xda-developers.com/android/apps-games/wayland-server-android-t3902720/Graphics performance is average, 3d acceleration is not available. Plus part of the resources is consumed by android. Not the best option for PC-1, but if you are linux lover you need to know about this way because it also works on most android smartphones and tablets. I often use Fedora on my old handheld.
4.2. No android / sunxi kernel / proprietary drivers. Sunxi kernel is the special linux kernel that was modified to work on allwinner devices. Actually, this is the kernel that is used for current (android-based) PC-1 firmware. It can also be used to run desktop linux distribution. May need to be recompiled with different config probably. But such kernel has "proprietary" drivers in it (kernel space) that can only work with proprietary user space libraries. If you are going to use such kernel with regular linux desktop distribution and want 3d acceleration to work, you will need to download proprietary user space components (libraries) and replace "free/opensource" libraries because "free" libraries can't work with proprietary part in the kernel. I didn't try this option to be honest. Graphics performance should be good. 3d acceleration should work partially (GLESv2, but not full OpenGL). Also this sunxi kernel is outdated in some way. We only have 3.x and 4.x versions while mainline kernel is 5.x for long time already.
4.3. Yay, the most fun part. No android / mainline kernel. Mainline kernel is the kernel from Torvalds' repositories. Its constantly updated and improved. Support for new hardware is added every day. Bugs are fixed. And it already has almost full support for Allwinner H3. All drivers are free and opensource. No need to replace any libraries in your distribution because "free" userspace libraries work with "free" kernel space code. I failed to setup NAND (PC-1 internal memory) and hardware video decoding on mainline kernel. Most of other function work: 3d acceleration (almost full OpenGL), audio, fast graphics output, wi-fi, etc.
Its really bad that I was unable to achieve hardware video decoding. Without it, playing even 720p video takes all PC-1 CPU resourses. 1080p can't be watched at all.
OpenGL is fun. I was able to run Open Arena (Quake 3 like game), ARM version of Homeworld (famous 3d space strategy), Doki Doki Literature Club (very strange game). All these run pretty smooth. And any games that don't require 3d of course.
Full guide on creating firmware from scratch will be too long. Basically, you need to:
1. Partition and format the sd card. At least one FAT partition + one ext4 or btrfs partition. Swap partition optionally.
2. Compile mainline u-boot (kernel loader). There is no config for PC-1 in mainline u-boot so you need to make one. You can use config from another H3 board as starting point.
3. Write u-boot to your sd card. You also need to learn a bit about boot.cmd file that will tell u-boot how to load kernel. This file is placed on the first partition of sd card.
4. Pull, configure and compile mainline linux kernel. Like with u-boot, there is no usable PC-1 config in mainline kernel so you need to make one. Probably, by extending sunxi_defconfig. Besides this, you need to write dts (also config of some kind) file for PC-1. You can start with dts file from some other H3 board, but still this task is not for newcomers.
5. After the kernel is compiled, you need to copy zImage to your first partition. Together with dtb file (compiled version of dts). boot.cmd needs to be updated with kernel and dtb names and compiled to boot.scr.
6. You need to bootstrap rootfs of any ARM linux distribution and extract it to second partition. You also need to specify this partition in boot.cmd and write /etc/fstab.
7. Don't forget to copy kernel modules to your distribution's /lib/modules dir.
Detailed guides are here:
linux-sunxi.org/Mainline_Kernel_Howtolinux-sunxi.org/Mainline_U-Boot