It depends on specific device and its architecture.
Those that are built on top of Android, typically tend to get AOSP ports, e.g. Nook (here's Simple Touch instructions), or Kindles - the latter even has CyanogenMod ROM.
Sony PRST 1 was hacked to expose full underlying rooted Android but I'm not sure if AOSP based ROM is available for it - this might be ...
If you sync via WiFi you should get version 5.2 build 1894. You can check if you have that version via the Settings → About ... menu.
The manual download page might be out of date with the actual version of CybUpdate.bin you download from there, or the download itself might be the 1780.
I have never tried to install that 1780 version as my Bookeen ...
Yes, they do!
In fact at this page you can find the update for your kindle (if it's not a kindle touch, then it's called kindle 5th generation), with the following information (bold is supplied):
We have a new, free software update available for your Kindle (5th Generation). This update automatically downloads and installs on your Kindle when connected ...
KOReader is an ereading software available for several devices and platforms. Quoted from Mobileread wiki:
KOReader is a document viewer for Linux based E Ink devices. Currently
there are versions for Kindle, Kobo, PocketBook, and Android devices.
The installation procedure depends on the device. Support forums are available on Mobileread.