In system.log, com.apple.cloudkit.pcs.flushCaches errors in log

... but is a sign of something untoward happening.

What events led you to that assertion? You will find plenty of cryptic messages in system.log.

Nov 17 15:03:01 zeus cloudd[562]: notify name "com.apple.cloudkit.pcs.flushCaches" has been registered 40 times - this may be a leak

Nov 17 15:03:39 --- last message repeated 4 times ---

I have no idea. I have seen that message occur but not to the degree you're describing. Try signing out of iCloud and signing in again. I have nothing else to suggest regarding that message. No one outside of Apple could possibly know what it means, so the proper action would be to contact Apple and describe the problem you're experiencing. Apple will only be interested in operational concerns though, and if they need to gather log data from your Mac in an effort to address those concerns they will provide appropriate instructions.

Could be the cause of the slow folder display when I open Finder? Open finder, it's default folder is Applications, and it often takes up to 30 seconds to display the entire list of apps.

That's unacceptable. Consider the following two suggestions:

1. Try safe mode if your Mac doesn't finish starting up.
   • Compare how your Mac works in Safe Mode to how it has been.
   • Then, restart normally. If the same problem returns, please read the section If an issue doesn't happen in safe mode for Apple's recommended actions.
2. How to test an issue in another user account on your Mac.
   • When you are finished troubleshooting, you can remove the temporary User Account by following these instructions: macOS Sierra: Delete a user or group.
   • Before removing it, confirm you don't need any of the files you might have created in that Account.

Time Machine has been failing - and I've tested and checked the external drive. Can't see what the problem is? Fortunately I have CarbonCopy to another internal HDD as well, so it's protected in that sense.

As long as you maintain redundant backups, a hard disk drive failure is a non-event that should be expected. Testing and / or "repairing" them with any particular utility is generally pointless. If you have reason to believe the drive is in a failed state, you might try erasing and reformatting it, followed by adding it to your Time Machine rotation again. If it has failed whatever caused the failure is likely to occur again, perhaps in a very short period of time, and the failure will reappear in increasing frequency. That is the usual hard disk failure mode.