Question about picture

Here you go: How to repair a Mac disk with Disk Utility - Apple Support

"Repair volumes, then containers, then disks"

DU has nothing to to with TM other than formatting a drive. DU works on the actual drive itself ... repairs, partitioning, erasing and so forth.

The drive you need most to backup is generally the internal one. If you're not using TM then what are you using? DU is not a backup utility.

What makes you think your HD is experiencing errors?

You have several thoughts here: drive errors, drive fixing, backing up, partitioning and Time Machine. What is your ultimate goal? Not all of these thoughts are needed to do a thing. Pick what you want to do and the order in which you want to do them and proceed. But you have to make up your mind where to start.

Good luck.

You have to know exactly what you want to do and communicate that here. There are many things you can do in DU, some of which are disastrous.

Decide what you want to do, if anything, and state that. It's a very bad idea to go poking around in DU without having a clear understanding of what you want and what you are doing.

There is no need to routinely use Disk Utility's First Aid. Just keep using Time Machine.