Unsure how to setup arch linux

I’m trying to installl Arch Linux on a chromebook, in dual boot, but I’m unsure how to define disk structure an how to install Grub.
I’d like, for now, to use it in dual boot mode, keeping the ChromeOs until I’m sure Arch woks well.

Following the MrChromebox.tech instructions I’ve successfully installed the RW_LEGACY Firmware,
shrinked the os disk occupation with the CRAP utility, and got so a large (32gb) free space.

The boot with the arch pen drive goes smooth, and I’m able to start the cfdisk program that shows me the
format of the internal emmc drive, containing 12 partitions and the free space available.
The structure of the disk is in gpt partition style.

Now its not clear to me how to setup the partitions, so I proceded as it it was a standard UEFI machine.

I tried to make two partitions, the first of 300mb (part 13)
and the second with the remaining space (about 28 GB) (part 14)

Then I mounted part 14 as /
and part 13 as /boot.

The installation of Linux went ok, the trouble started when I tried to install grub
I issued the following command:

grub-install --efi-directory=/boot

The command returned no errors, so I tried to boot the machine, pressed Ctl-L at the developer mode page,
but my linux instance was not shown.

Since the firmware is RW_LEGACY, how should I install GRUB, without destroying the boot sequence ?
Can I try to install it on the MBR of the disk (if Yes, How ?)

There is a chance to damage the machine and render it unbootable ?

Any suggestion ?