Gillespie,
It appears that you have a corrupted system. Please do a full Restore as described in the article below. While this may seem daunting at first, it is rather straight forward as iTunes will guide you along the way. You will have to disable Find my iPad first. Don't forget to set it back to On when you are through.
You will be connecting your iPad to your computer. Then import all your photos from the iPad to the computer and backup all important documents to your computer HD. Then do a full backup to iTunes, just follow the instructions below. Then select Restore iPad and iTunes will install a fresh copy of the current iOS and will erase all your data. After iTunes has installed a fresh copy of the iOS, it will ask you if you want to set your device as New or restore from Backup. Choose From Backup. Restoring will bring back all your Settings, Apps, Photos on Camera Roll, etc. You should not lose anything.
After completion check to see if all works well. There is a possibility that restoring from the backup may bring back the offending Apps and their data. If that occurs you would have to start over again, set it up as New and install all Apps manually (a time consuming process). You would also lose your photos and documents so it is important to back them up first as I mentioned above.
I have done this myself several times and restored from backup with no difficulties - it takes 30-60 minutes.
https://support.apple.com/en-us/HT201252
