The reason you can uninstall updates to system apps is because of the way system apps work. There's the original copy of the app which came with the ROM, which cannot be changed except by a system update. Any updates are installed in /data/app, the same as user-installed apps, and in effect "take over from" the pre-installed copy. So if you uninstall the update the pre-installed version is still there.
When a user app is updated, the update replaces the copy in /data/app. As that is the only copy, uninstalling the update would be exactly the same as uninstalling the app, which is why that option isn't there.
For the same reason, when you uninstall updates to a system app you go all the way back to the pre-installed version, no matter how many updates it has had since: each update replaced the previous one, so you cannot just roll it back one version, all you can do is revert to the pre-installed one.
So if you want to revert to an earlier version of a user-installed app your only way is to find an apk of the older version and install that. The trick is finding a safe source. Apkmirror.com is one, but since it is a reputable source it only has back copies of apps whose developers allow this (which is quite a range, but not all). If an update is causing problems you could contact the developer, since they will sometimes let you have a copy of the previous version in these cases.
As for making any app into a system app, that requires installing it to /system, which requires root privileges. If you have root, then Titanium Backup can in principle move apps ("in principle" because it's a long time since I did this, and never with an odexed ROM, so I'm not going to promise success). I would strongly recommend using a custom recovery to make a backup of the ROM before making any changes to /system, including moving apps into the ROM.