You should actually be able to ignore those driver errors when installing. I've had a few kali 2.0 installs with my laptop where i get that error for both ethernet and wifi drivers, i choose continue, and it connects 5 seconds later. The drivers built into the iso should be able to handle your hardware. And with kali 2.0, i actually don't think it's that important to be connected during installation anyway. Just make sure your /etc/apt/sources.list file has the correct repo's after install. http://docs.kali.org/general-use/kali-linux-sources-list-repositories
When you get those error screens on bootup, try pressing ctrl+alt+F1 to drop back into the console. If i had to guess, you're issue is your graphics driver cuz that's happened to me b4. You should be able to sort out your install from the console. Is your gpu nvidia? http://docs.kali.org/general-use/install-nvidia-drivers-on-kali-linux
. It can take a few weeks and a few tries to find the right driver/kernel combo for nvidia laptops, i speak from experience. The kali repo's have a few different options, and there's also the option of downloading the driver's .run file from nvidia website and installing from teh console screen.
When you're in the console, typing 'journalctl -xn' should give you some idea where the error lies if it's not a graphics driver problem.
Have you reformatted since you took those screenshots?
Edit: Just noticed that you said a separate "/home" directory. In kali installlation, you're home directory gets installed to //root. 2 slashes.