I would like to narrow this down to what specific hardware failure I am dealing with before investing money. Someone else has been suggesting I get an external SSD. How do I confirm that the HDD is the problem, and, if it is, then will an external SSD (most likely) solve it?
If a CPU overheats, then the entire computer powers off (a "halt", not a graceful shutdown), from my experience. Misbehaving fans can cause the CPU to get hot, which is not happening in your case according to the sensors output. Your CPU temperature is in fact quite normal.
But basically, the internal hard disk (hence the "ata" in the messages) is the problematic part, and you should swap it with a newer internal hard disk - HDD or SSD - whatever your PC supports, doesn't make a difference in stablity really - make sure the new disk is not like 5 years old though
.Plugging external disks will not make the problem with the internal hard disk go away.