After a ton of tests and a deeper investigation started from @oldfred useful insights, I think I solved the issue. In this answer I just want to briefly describe how I managed to accomplish that and the findings of my investigation.
I managed to boot my dual boot (Kali + AVLinux) system on every PC of mine, either only BIOS booting capable, only EFI booting booted or both.
The major requirement to do that is installing grub either in BIOS mode AND in EFI mode. This can be accomplished preparing the device/disk in such a way that it uses a GPT partition table and then creating a BIOS_BOOT partition as well as an EFI system partition at the beginning of the device. They're easy to create as there's plenty of material on creating both types of partition on the web. (e.g. BIOS_boot partition, EFI partition).
I attach a screenshot of my device partitioning, hoping to make it clearer:
I now address the topic splitting it to the EFI boot part and the BIOS boot part
EFI Boot
As I said in the question, I also installed (for EFI boot mode: i.e. booting my VirtualBox VM enabling EFI*) the first distro (Kali Linux) of my dual boot system simply using its installer by a VirtualBox VM with its .iso file loaded as the content of the VM optical drive.
The installation went all good, except for the fact I wasn't able to boot my system in any machine (maybe apart the same VM which I used for the installation, but I'm not completely sure).
The reason for this was that the grub-install ran by the Kali installer placed grub inside my EFI partition in the /EFI/Kali/grubx64.efi path, while, as @oldfred suggested:
external devices only UEFI boot from /EFI/Boot/bootx64.efi.
This is why I managed to boot the system moving+renaming the boot loader located into the EFI partition from the /EFI/Kali/grubx64.efi path to /EFI/BOOT/bootx64.efi path.
Also, further investigation showed me that we can get rid of the problem reinstalling grub (f.e. following the metodology showed in this question) and adding the --removable parameter in the calling of the grub-install command.
the command on the guide would therefore become:
grub-install --removable /dev/sdX This will place the boot loader into the /EFI/BOOT/BOOTX64.EFI path, solving the problem.
* This is pretty much the same of running the installer on an EFI boot capable PC
BIOS (Legacy) Boot
Once a BIOS_boot partition is created, we have to install grub for BIOS boot mode (a.k.a. installing it in the MBR) through grub-pc package*. The procedure is pretty much the same of the one used for installing grub for EFI boot mode, unless we DON'T mount the EFI directory:
sudo mount /dev/sdXX /mnt/boot/efi
and we specify the i386-pc target platform in the grub-install command:
grub-install --target=i386-pc /dev/sdX Actually, unless I read that grub-pc package is for installing grub in MBR (so for BIOS boot mode) and grub-efi package is for installing grub in the EFI partition (so for EFI boot mode) I'm not 100% sure about this, since I managed to install grub in the EFI partition with grub-pc package installed as well