Thanks for all that detailed information. It looks like both your wife and you have useful tasks that you are using your iMac for. One question, though, is what is the "Disc care app"? I've never heard of that one.
I believe I can answer one of your questions. I suspect that Numbers and Pages should be "basically" the same. I do not use either of them, as I have Office 2016, and thus use Word 2016 and Excel 2016 (and Outlook 2016 for my EMails). But when I upgraded from Office 2011 to Office 2016, everything was seem less with all 3 programs. However, I have always made sure that the version of either Office 2011 or Office 2016 was/is current.
One other thing is that your version of Google Chrome is behind. I use Google Chrome as my primary browser, and I rarely, if ever, use Safari. The current version is V 64.0.3282.119. If you want to upgrade, it is simple: when you launch Google Chrome, move your mouse pointer where it says "Chrome" (upper left hand corner), click on it, and then select "About Google Chrome". It will take a minute or so for the update to be downloaded, and you will then be asked to relaunch the program.
As I mentioned, I use Outlook 2016 for my EMail needs. I have seen reports here of folks having difficulties with Apple's Mail program, and a number of those happen after an OS upgrade. However, I wonder if a lot of that has to do with improper planning with the upgrade.
In any event, Sierra, OS 10.12.6, is definitely a stable OS. To prepare for the upgrade, here are some things you need to do:
1. If your wife or you are using any third party (ie, non-Apple) applications (except browsers, like Google Chrome, although she should upgrade), you'll need to insure that they are compatible with Sierra. This link will help you with that:
https://roaringapps.com/apps
2. For the next two steps, you are already doing them (as long as the Disk care app" is "OK"): perform disk cleanup/maintenance/repairs, from a software perspective, and then do a final backup. For disk cleanup/maintenance/repairs, you actually can do a good amount of disk cleanup on your own, and there are also some excellent third party programs available (both free and commercial) that can help you with that.
3. The next step is how you want to upgrade to Sierra, OS 10.12.6. There are 2 choices: perform a clean, fresh, "virgin" installation of oS 10.12.6, or just upgrade from OS 10.11.6 to OS 10.12.6. There are Pros and Cons with either approach. Myself, I always do a fresh, clean installation of the new OS (or sometimes when an upgrade to the current OS is released). However, I do make backups differently that you (and quite a few other folks on this site). I use SuperDuper!, which make a bootable clone of my system. I have found that for either an OS "upgrade" or a recovery, using a SuperDuper! backup makes either of those processes smoother, along with me having more control. I actually started a thread about backups back in November, and you might want to have a look at it. Here is the link:
https://www.mac-help.com/threads/backups-backups-backups.223959/
As mentioned there, you can use either SuperDuper! or Carbon Copy Cloner in demo mode, and the full functionality of the bootable backups will be there.
Unfortunately, the "stickler" with a clean, fresh installation is that you would need the "Install macOS Sierra" file, which "should" be available from the App store. But Apple, in their "?wise?" wisdom, has chosen not to make that file "easily" available (I actually have it, and that's because after I first downloaded it (when Apple had not yet changed their "thinking"), I made a copy of it before proceeding with the installation).
So, come back with more questions, and I (and others) will be glad to help you. Also, some other folks hopefully will "chime in" about Mail, upgrade versus clean, fresh installation, experiences with newer versions of Pages, Numbers, and Safari, etc.