10 year old iMac is Dying. How do I ensure that Time Machine is backing up EVERYTHING?

Nine hours? This hard disk has passed “dying”, and has reached “dead”.

The iMac 24” is the direct replacement, if you don’t go external SSD and decide to replace.

Biggest difference with the newer iMac 24” is the use of USB-C connectors (there are docks and dongles) and the number of USB-C connections available.

Mac mini and Mac Studio are the Mac alternatives to the iMac 24”, and Studio is probably (much) more than you need; well past a Core i5 configuration.

Memory and storage cannot be upgraded on recent Mac. Go 16 GB memory, minimally. Go as high as you can reasonably afford, as you do seem to keep these Macs for a ~decade.

As it comes up in these topics and as yours is in the right range, an older and pre-retina iMac can be used as an external monitor, but 2020 and newer Mac is not compatible with that older iMac used as a monitor. Details: Use your iMac as a display with target display mode - Apple Support. Put differently, you’ll need an appropriate monitor for a recent mini or Studio.

You don’t and cannot be sure what gets copied, to be blunt. The more you try to back up, or to repair, or just use this storage, the more likely the underlying storage can and will fail. You’re likely already losing data. Failing hard disks can tend to fail progressively, though the rate of that failure can vary.

If you have a Time Machine backup that’s been around for a while and has some depth, you probably have enough to recover, particularly if the new Mac adopts the old backup, a d you can then revert to an older copy should you encounter a corrupted file.

Your options are to repair (expensive, not worth it here), or an external storage device (Thunderbolt is decently fast, USB 2 not so much), or replacement.

Here’s a write-up on external boot: How to Setup and Use an External SSD as y… - Apple Community

Disable the cleaner app. That general type of app can cause issues, and that type can also cause added I/O activity here. (I’d usually remove it, but your priority here should be on migration, and not clean-up, diagnostics, or otherwise.)

Time Machine will backup everything assuming your external HD is in good working order. To test it, simply attempt to restore a file or a number of files. In the 20 years I have been using Macs I have found Time Machine to be reliable and stable. It is not perfect however I have not experienced any issues that were not easily fixed. Also, I recommend getting a new Time Machine External Hard Disk about every 4-6 years, why simple ALL HD's wear out and it wise to be proactive so you are not caught without any backup. It is also a good idea to do redundant backups such as using Time Machine and a cloning app such as Carbon Copy Cloner or SuperDuper! to ensure you always have a backup. That way you are sure if one External Hard Disk dies that you likely have another backup plan until your can replace the failed External Hard Disk.

When you buy your new Mac please follow the steps to migrate from your old Mac to the new one. The directions are in Setup Assistant and Migration Assistant.

I will offer some thoughts which you may find useful.

• Always backup to an external disk.
• The Time Machine app does not back up your email files. To do that you must use another app such as Carbon Copy Cloner, which does.
• You can specifically control your backups by doing them manually yourself. Whenever you add or change a file, just copy it to your backup folder to replace the older file.
• Since your computer is failing, replace it before it completely dies. That can make it less stressful to deal with moving your files to a new computer.

Time Machine does back up mail.

https://www.macobserver.com/tips/quick-tip/time-machine-lost-email/