While deleting apps to free up storage, I removed important system functions (display touchscreenscanning). How can I replace the system with a fresh version of Android 4.2.2?
If your goal is to have a fully-functioning device again, you should be able to do a factory reset to return to a factory image. If you did not root, then your system image should be ok.
Navigate to Settings > Backup and Reset > Factory data reset and proceed from there. This will delete all data on the device, but your installation of Android 4.2.2 will be fresh, just when you started using it.
You need to find a complete ROM for your tablet and flash it. Basically:
1. Search Google for " stock ROM" if you want the exact same system. Make sure you get the "gapps" (Google Apps) for that version of Android.
2. You will need a custom recovery, so search Google for " custom recovery" (TWRP and CWM are 2 common recoveries).
3. Find the instructions to flash your tablet