HP P840 HDD RAID 5 many strange drive failures

You probably have an heavily punctured array, which cause an early "planned death" of the replacement disk due to failed stripe reconstruction. You can read more information here and here

The solution is to backup, destroy the array, recreate it and restore from backup.

Next time avoid using a RAID5 array with such big drives. I strongly suggest using RAID6 or, even better, RAID10.

You should be using RAID6 with the size and types of disks in the system. However, there's nothing inherently wrong with running RAID5 on HP Smart Array RAID controllers. I think your issue is a result of using consumer disks in a setup not certified for the server hardware.

Some details about the server may be helpful, though.

Is this an HPE server, or are you just using an HPE controller?

These don't appear to be HPE drives or HPE drive carriers. That's a bad sign.

The hpssacli output you've provided would also show the reason for the disk failure. If you're not on an HPE server and there's a backplane issue or SATA timeouts (noticed you're on SATA disks), there's chance that you're getting false positives.

Example: (see the Last Failure Reason line):

  physicaldrive 2I:2:8
     Port: 2I
     Box: 2
     Bay: 8
     Status: Failed
     Last Failure Reason: Aborted Command
     Drive Type: Data Drive