enluk, A few questions:
Is this a dual booting machine?
Has the install media been verified with the checksum, or has it been shown to work elsewhere?
That partition arrangement in post #52 is for a UEFI installation, but has no swap partition, so, if you wish to have a swap partition, a new partitioning would be necessary.
Installing the latest BIOS/UEFI was likely the best thing to do, since presumably the manufacturer thinks so.
The problem with the install disk booting to initramfs is usually a problem with the install media, or a problem with the disk such as bad blocks.
Since I presume there is no linux installation yet on the laptop, my inclination would be to verify the media in the first instance, and start again.
Nevertheless, with the initramfs prompt, you can see what it says by typing: help, which should give you a list of commands that it will accept. Then you can run some and see if the output is helpful.
One of those commands is likely: exit. After typing this command, the output on screen may actually indicate some problems that it detects. If it has detected bad blocks on the disk to be installed on, then you can run something like: fsck -y /dev/sda2, and see what can be fixed. Then just run: reboot, and with the install disk still inserted, there may be a different result. Maybe not though.
I can't say whether any of this will be useful, but for success there must be certainty that the install disk is good.
It's worth noting about that UEFI partitioning shown in post #52 without the swap partition, that you may be better advised to choose manual partitioning in the installer if you wish to make the partitions according to your preferences, or use a live disk to partition the disk before using the installer and having the installation use that now pre-existing partitioning.