Various applications are crashing on my iPad, including Facebook, Safari, and TwoDots, along with others. I have tried all of the solutions I found except doing a factory reset and downloading the backed up iCloud version of the iPad. What do I do?

When I try to open or access some features of these apps, I get the

loading sign, then the screen turns black, and it takes me to my Home screen. Sometimes this also occurs when opening links in Facebook and Safari, and some of my Apps are completely useless as a result of this. I have rebooted thrice, re-downloaded the apps, and tried clearing them from the queue, nothing works. Also, I have noticed that the background of the home screen is oriented incorrectly at times, (background is portrait whilst the rest of the screen is landscape) and I'm really at a loss. I assume it's a glitch with iOS 7.1.1... The iPad is a 4th generation and has shown no problems until recently, around when I updated. I'm not jail broken or anything, but my Wal-Mart warranty has expired. What should I do?