Many thanks for sharing all those photos.
The system has detected some filesystem corruption and it doesn’t want to automatically repair it, since there is a risk of data loss during the repair process.
I suggest first booting an Endless USB disk (or another Linux distro USB) and use that to attempt to access your laptop hard disk and backup any important files on separate media (when browsing the disk, you’ll find your data under “home”). Even though there is some filesystem corruption, most likely you can read files off it.
When you’ve taken a backup just to protect us against the worst case scenario, boot Endless again, and when you get to this error screen, carefully run:
fsck /dev/sda3
You’ll be asked to confirm that you want to fix several filesystem problems, just say “yes” here.
If you could take some more photos throughout that process it would be much appreciated, might give us some hints as to what happened.
After the repair is complete, run reboot and hopefully you’ll boot back into Endless again. Check that your files seem intact.
I’m sorry that the handling of the filesystem corruption here is sub-standard, we’ll work on improving this for the future.