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Which step does fail?
apt-configuration or another?

I just made a quick experiment with Conky. This fits your image of "Screenlets" quite well:
http://oi60.tinypic.com/34erkv4.jpg

This is just a really simple setup. Combinig it with shell scripts...

I haven't used them in Kali, but since it's based on Debian and GNOME 3 you may install them as you would in any other Debian-based distro (Debian itself, Ubuntu, Mint, etc.).

no, it didn't have all the tools installed. I didn't check through every single one, but the most useful and often-used ones are there. You can always install missing tools, as long as there are...

can you disable EFI and swith back to an oldschool BIOS?

Did you use the generic armhf image or the dedicated RasPi one?
I just recently have set up one of my Pis with Kali again and it worked right out of the box.

I guess you extracted the .xz and...

That's actually not a bug. Just normal bash behaviour. I don't know of any way to select and copy displayed text directly, except for some editors (like vim or emacs) where you can do such stuff form...

Could be an UEFI-problem, but since you can reach the login-screen and actually interact with it I think it's unlikely.

Can you live-boot Kali from the thumb drive? If so, mount the HDD and...