The error message visible in your first and forth screenshot explains what is causing your issue:
Failure: File system check of the root filesystem failed
It also tells you what is needed to fix the problem:
The root filesystem on /dev/nvme0n1p2 requires a manual fsck
Thus what you will need to do is type the following command at the (initramfs) prompt:
fsck -yf /dev/nvme0n1p2
This will check your root filesystem for errors and fix them, I would recommend running the command again if any errors are found to verify the filesystem is healthy.
One other concern however is that you mention this is happening repeatedly, this really should not be the case. One potential cause of this other than repeatedly improperly shutting down your system could be a dying disk drive.
If the issue continues to recur then I would suggest taking the time to perform diagnostics on the drive to check it's health. There is already a good answer elsewhere on the site explaining how you can go about this so I would suggest reading here for help with that How to run a checkdisk?
Note that a failing drive could also be the cause of the other freezes you mention so I do strongly recommend taking the time to run the above diagnostics as soon as possible. This will also give you chance to safely back up your data before the drive fails completely in the event that it is on it's last legs.
