I'm struggling to install Kali 2017.1 on an old HP8440p in dual boot with the existing Windows10 partition.

First point: non-UEFI vs. UEFI.
The laptop's BIOS does have a UEFI option which was NOT enabled at the time I made the first installation attempt of Kali (and was NOT enabled when I upgraded the OS from Windows 7 to Windows 10).
Actually it was never enabled and even did not know it existed or what it meant before I started experimenting with Kali.
Although I enabled the UEFI option in the BIOS setup after the first unsuccessfull installation attempts of Kali, the installations still kept failing afterwards (see below).

What I did (with UEFI Bios not enabled yet):

Main scenario (preferred as I want to avoid using Grub on the MBR)
1) The HP8440p has a factory "TOOLS" partition (showing up in Windows as drive E which I resized in order to have 20Gb available for Kali. I could have carved out space from the main "WINDOWS" partition on C: but I decided to use "TOOLS" instead as I thought its available free space (20GB+) was a waste of storage. The physical drive is a single solid state 500Gb Crucial disk. The free space I reserved for Kali is then located approx after the 400Gb boundary on the drive, in case it matters.
2) Downloaded and imaged Kali 2017.1 to a USB drive and booted from there
3) Run the graphical installer and used the free space made available at step 1) to create three logical partitions:
a) /boot (4Gb) /dev/sda6
b) / (10 Gb) /dev/sda7
c) remaining 6Gb as swap

4) Set the Grub loader to install on /dev/sda6 (not the MBR) and finalized the installation

5) Rebooted to Windows 10

6) Used EasyBCD to configure a Windows-based dual boot menu: Win10 and Kali

7) Rebooted and selected Kali in the boot menu

8) Laptop restarts and the dreaded GRUB Minimal bash like shell appears

Alternative scenario
1) -3): same

4) I choose to install Grub on the MBR

5) Rebooted: the Grub boot menu appears (showing also Windows10)

6) I select Kali: the OS boots correctly! I thought I made it

7) Reboot again and select Windows10 option: Windows starts fine and I think I'm done

8) Reboot again into Kali: FAILURE!
A bunch of file system and drive related errors are displayed and I'm now in a Busybox shell.
Apparently rebooting into Windows caused something in the setup that Kali and/or Grub did not like

I also re-run the main and alternative scenario after enabling the UEFI option in BIOS with exactly the same results.

I evidently don't know what I'm doing and I'd appreciate some help.

Thanks in advance!