Does restoring from Time Machine backup not fix system problems?

So do you think the first step might be to do a full Time Machine backup restore and see if the problems I'm seeing are gone?

Actually, what Disk Warrior is telling you is that your Mac's hard drive may be corrupted. It may be so because it is either faulty or starting to fail. You didn't mention which exact model iMac that you have or how old it is.

I don't use Disk Warrior so I can't give you any step-by-steps, but it should have the option to check your Mac's hard drive throughly for errors. Alternatively, you can use macOS's Disk Utility or another third-party app to do this.

Once you verified that the drive is NOT faulty, I would suggest that you run EtreCheck and post the resultant report so that we can take a look at the "health" of your Mac.

To help troubleshoot your Mac, I would suggest that you consider using EtreCheck and posting the resultant report for us to review.

• You can download EtreCheck from here.
• Start EtreCheck from a normal user account. Optionally, you can run it from a user account with Administrator privileges.
• Select Options

  Verify that the two options: "Ignore expected failures in Apple tasks" and "Hide Apple tasks are enabled." Note: They should be by default. You can skip this step the next time your run EtreCheck.

• Select a problem from the drop-down menu to enable the "Start EtreCheck" button. Optionally you can add comments on what you are experiencing, especially to aide others with if you post the results.
• Click on Start EtreCheck
• Allow the program to run to completion.
• When done, you should get a results report.
• Select the "Share Report" icon.

  Select Copy Report

• Paste the report to your reply post.

Finally, if both the drive and EtreCheck show no faults, I would second your suggestions to perform the restores in the order you listed them.

I'm hoping that maybe Time Machine will fix any system problems it sees, but have no idea if that's just wishful thinking.

In itself, restoring from a Time Machine backup, may or may not fix system problems. It will depend on what the problem actually is. However, it may be possible to restore individual files or the entire system from these backups.

Would the thing to do be to restore the OS completely, and then somehow bring over all the files outside the system?

Again, it will depend on what issues you are having with your iMac. Reinstalling a "fresh" copy of the OS would be considered the "most drastic" measure but shouldn't be performed until you can first verify that there are no hardware issues present.

To answer your question more directly, you could put your iMac into either Recovery or Internet Recovery mode to restore the OS. Then use Migration Assistant along with your Time Machine backups to restore your applications and data.

The problem is I have a ton of software (music) that I think creates system files? Not sure. And if so, then I would lose all that/have to reinstall many things?

That may be a possibility, but restoring from a Time Machine backup should prevent this from happening.

I'm in the middle of doing a couple of things that had resulted in problems (one is a large file download and installation), and if they turn out ok, do you think I'm out of the woods regarding 1) the drive being potentially damaged

The "100%" results are a good sign, but I would suggest that you consider adding disk cloning to your backup strategy if you don't already do so. That way, should the internal drive fail for any reason, you can quickly get back up and running from the cloned drive.

and b) the system being back to functioning well?

Sorry, but there is no way to guarantee that. If the last backup that was restored was at a point where there were no issues with your iMac, then it should function as well as when that backup was made.