imac not operating correctly after OS install

Bring it back to service. An erase and install should allow storage to be visible.

And bring the external drives with you.

They can verify if the problem is with the drive or the computer by isolating the probelm on other computers.

One thing to note, Energy Saver doesn't work well with peripherals. Use screen saver if possible instead of sleep/energy saver, which has a put hard drives to sleep option.

External hard drives that don't have their own source of power may not connect as other peripherals may over load the USB bus. Trying different ports for the drives can help. Adding a wall powered USB hub can also help if the drives don't have their own source of power.

Is your mouse a wired mouse, or wireless mouse? Does it use its own transceiver that is wireless, or use the Mac's own built-in Bluetooth?

If you installed any software like Mackeeper, Advanced Mac Cleaner, or any Macpaw or Zeobit software, that's the reason why your system preferences are unstable. These software ruin system caches. They should not be used.

Use Etrecheck to get a diagnostic of the background applications, and report back here:

Etrecheck - the handy reporting tool for … - Apple Community

Use a wired keyboard and mouse until you identify the source of the problem. If you can't with wired keyboard and mouse, then bring it to Apple. Note, any repairs Apple does typically come with their own warranty. Call the Apple Store for verification.

Restart in Safe Mode, install Etrecheck and run it.

There could be a hardware problem, but there could also be some third party software that is wreaking havoc on your system.