Q: Need Urgent Help Diagnosing Problem

I would say good morning, but it's not. I'm starting to panic that my MBP's dying and, after exhausting virtually all of my options, have no idea what to do.

All of a sudden, with no noticeable program or action triggering it, my late 2011 MBP (13", 8GB RAM, 512GB SSD) has collapsed. I can boot it and it works for 1-2 minutes before permanently beachballing when I try to do anything and everything becomes unresponsive, requiring another reboot. Happens every time it's rebooted and makes it near impossible to fully complete any recovery/backup/troubleshooting attempts.

This extends to Disk Utility and any attempts I've made to create a bootable USB. Trying to run on First Aid, it always hangs on Checking Catalog File, sometimes Disk Utility won't even load the disks before beachballing and requiring rebooting.

Things I've tried that have failed/encountered beachball during:

- Erasing hard drive (SSD doesn't appear in Disk Utility in recovery mode to erase, appears in Disk Utility when booted normally).

- Installing macOS Sierra on formatted external drive (didn't work initially but is currently appearing to be working, taken about an hour to reach the half way mark so far).

- NVRAM/PRAM reset, successfully executed but made no difference.

- Backing up to external drive via Time Machine (everything beachballs before it even comes close to completing backup).

- Changed RAM, ineffective.

There are probably other things I've tried that have failed as well, I'm starting to lose track of what I've desperately attempted. I've tried pretty much everything I've read in terms of troubleshooting. The MBP just seems incapable of executing any task, no matter the size or effort required. Any help would be greatly appreciated, thanks.