Kali Linux Live Flash Drive Does Not Detect My SSD

[Abs0lute]

Hello everyone,
so, i'm new on this forum and globally in forums posting so i first want to apologize for every mistakes i will surely make.

So here is my problem, i've got a Notebook AsusPRO BU401L with a HDD of 500Gb and a SSD of 128Gb on which i had a multi boot with the last version of Kali Linux (on the SSD), Debian, a partition for data and a partition of Windows Recovery (in case one day i want it back) (on the HDD).
So all was perfect, i was doing my stuff on Kali (xfce environment if it is useful) until the day i tried to execute an exe file. (it may look dumb for you but i'm kinda a newbie so it was more of a test for me )
I don't really know if there is a link between my problem and that but after this try, my firefox crashed with no possibilities to restart it (by possibility i mean click on the web browser application icon). Then it was the menu button on the top left that didn't work and was displaying an error message.
With all those bugs i decided to reboot my laptop.
So i opened a terminal and type

reboot

but nothing happened, so i forced it with

reboot -f

.

The reboot took and eternity to finally end on the BIOS screen and not on GRUB as it should have been. It is there that i find out that all my boot options (such as Debian, Kali, even Windows Recovery) have all disappeared. There was nothing left, no even a single option.
So i didn't know what to do, i tried to put the CMS thing enabled also with the PXCE option without knowing what all this was about but it led to nothing.

At this point i took a bootable flash drive with a 64bit Kali Linux Live System (2019-02-14) on it to see if i could do anything once on it.
(

uname -a: 
Linux kali 4.19.0-kali3-amd64 #1 SMP Debian 4.19.20-1kali1 (2019-02-14) x86_64 GNU/Linux

)
But at this point, i faced another issue, the issue which is in the title.
Indeed when i was on this old Gnome Kali Linux, i noticed that my SSD wasn't detected. If i didn't knew it yet, now i can tell that the SSD was well detected in BIOS.

Here are the results of

fdisk -l

fdisk.jpg

lspci

lspci.jpg

and file manager :
FileManager.jpg


My request here is if there is any solution to go back to normal, with my grub, my Kali Linux and Debian desktops.
Or if there's not any, how i could access my SSD to backup my files before trying a reset of everything.

More details :
First, trust me i won't post anything if it wasn't my last option, as said i don't post on forums because usually i find my way of i just give up.
Maybe i didn't search with the good terms and maybe there is a topic with a solution for me and i'll be really glad if you have it.
On things that i found, there was a forum where they said that you have to put the option of SATA in BIOS on AHCI but i'm already on this option due to the fact that it is the only one they give me.
There are no partitions on the SSD, there are only some on the HDD.
Finally, sorry if there are a lot of useless data, i really don't know what can be useful or not and conversely, sorry if there are not enough informations.

I hope someone could help me. Thanks for the reading.

[Abs0lute]

Also i forgot to precise that when i boot on Kali Live there are many lines which say :

ata3 : link too slow to respond (something like that)
ata3 : COMRESET failed (errno=-16)

then it says that it stops trying and it boots.