OK, some more comments/answers to your questions:
1. For third party applications, it is important that you check whether the app is still compatible with OS 10.12.x, ie, Sierra. If it is, then the next step would be to insure that the version you currently have is either compatible, or that there is a newer version available that is compatible. It's best not to take a "blind" approach and just download whatever version is available. Most of the time (as long as the app is still compatible with the new OS you plan on using), that's OK. But it's always best to keep on top of things like that on your own.
Myself, I have 6
key third party apps:
SuperDuper!
TechTool Pro
Onyx
1Password
Office 2016 (mainly Outlook, the EMail program that I use)
Logitech Control Center (for the Logitech mice I use with each of my Macs)
In fact, I will not upgrade to a new Mac OS until
all of them are compatible (either as they are, or with updates (which seems to be always the case)). For the last two releases of the new Mac OS (El Capitan and Sierra), I did not upgrade (via a clean installation) to the initial version, as some of my third party apps did not have upgrades available at that time. So, for El Capitan, I started with OS 10.11.1, and similarly for Sierra, I started with OS 10.12.1.
2. I don't need to do daily backups, although that can be done with SuperDuper!. The thing about SuperDuper! (Carbon Copy Cloner is another, similar, excellent program) is that it makes an
exact, bootable clone of your system when you back it up. Note that I said
bootable. That means I can start either of my Macs from any such backup. It is actually like having another machine, ie, the SSD where I have the backup is like having another Mac! It definitely makes recovery easier, and similarly with what you need to go through. Recently I made a mistake on my MacBook Air, as I removed all my EMails in my In Box (and while on vacation, of all things)! Yes, definitely not smart! And with Outlook 2016, when I do a deletion of an EMail, I use a key combination to have it permanently removed/deleted. Well, I fortunately had a recent SuperDuper! backup (less than 4 days old), and after first saving some important updated items externally (transactions I had entered in Quicken, and some updates for software I had downloaded), I restarted my machine from the SuperDuper! backup, used Disk Utility there to Erase and Format the internal SSD inside the MacBook Air, did a fresh, clean installation of OS 10.12.4, and then used Migration Assistant to "migrate"/copy needed "stuff" from that latest SuperDuper! backup. I then restarted my MacBook Air, and was back in business. (I also recently did the same thing with my Mac Mini, but it was not due to a catastrophe).
I actually could have just used the Recovery feature of SuperDuper!, which would have avoided the clean installation of OS 10.12.4 (I have used that feature before, and it works fine). But given that it had been a while since I did a clean installation, I decided to proceed as I did. Maybe overkill, but that's OK.
Recovery is possible with Time Machine, but the process (at least to me) seems more involved, and not as straight forward as with SuperDuper! (or Carbon Copy Cloner).
3. As for disk cleanup/maintenance/repairs, first of all, I am, on a daily basis, doing disk cleanup. As I mentioned above, with Outlook 2016, when I delete an EMail, it initially gets placed inside the Deleted Items folder. I then use a keyboard combination (actually just holding down the Shift key while selecting Delete for items in that folder) so that the EMail/EMails will be permanently removed/deleted. No sense wasting disk space with deleted EMails.
Also, whenever a new version of an application comes out, after downloading and installing it, I get rid of the previous version. For example, yesterday a new version of 1Password was released. I downloaded and installed it, made sure it worked (as expected, it did, as that is a very solid application), and after saving that new version, got rid of the prior one.
Now, on a weekly basis (typically on Saturdays), I go through 3 steps as part of my disk cleanup/maintenance/repairs, and backup processing (I do this for both of my Macs). Here are the steps:
1. I run the excellent freeware program Onyx (available from here:
https://www.titanium-software.fr/en/onyx.html; make sure you get the correct version, ie, once you upgrade, get the one for Sierra). That venerable program has been around for quite some time, has had numerous positive reviews, and besides some useful disk cleaning (and some "basic" disk maintenance), one can also use it to Repair Permissions, a function that was dropped with the versions of Disk Utility in both El Capitan and Sierra. Supposedly, the OS "takes care" of permissions, but Onyx still finds permissions to be repaired.
2. Next, I run the excellent commercial program TechTool Pro (
https://www.micromat.com/products/techtool-pro). That is another venerable, solid, and well reviewed program that does more disk cleanup, "deeper" disk maintenance, and if needed, disk repairs. I would not be without it.
3. Finally, I run SuperDuper! and make two backups to two separate external devices (SSDs, in my case). I of course would not be without those backups!
By doing all that, I rarely, if ever, have issues with either of my machines, and both of them run "lean, mean, and clean". I always equate owning and maintaining computers to owning and maintaining an automobile. If one does not have required maintenance done on a car, sooner or later trouble will arise. Well, computers are no different. Besides, it's always beneficial to become more educated with such devices (actually, with most things in life).
As far as deleting apps is concerned, there is an excellent freeware program entitled "AppCleaner" (available from here:
https://freemacsoft.net/appcleaner/; again, make sure you get the correct version). It works very, very well in cleaning up just about all the additional stuff associated with an app (and of course the app itself). I certainly recommend it. Usually for "reputable" Mac apps, just deleting the app itself is OK, but as you can tell, I am paranoid about disk space ("lean and clean"), and thus I use AppCleaner.
One more remark (although I stated it earlier): I can understand why you wanted to upgrade from OS 10.7.5, but you skipped through 4 intermediate versions of the OS before installing Sierra. Yes, maybe things were OK, and maybe they still would have been fine if you had not interrupted the OS 10.12.2 upgrade, but that was still a HUGE jump. And especially when you had not been doing much (maybe none?) disk cleanup/maintenance/repairs. When Apple releases OS 10.13 (or whatever they call it), I will upgrade (again as long as my 6 critical apps are either fine as they are, or upgrades are released), but it will be via a fresh, clean, "virgin" installation of the new OS. I suspect given all that I do, that would not be necessary. But, it's the way I want to go.