First I thought about writing my own explanation, but here is one from androidauthority.com:
[quote]#####What is rooting?
Rooting is the process by which you regain administrative access to your phone. Even though Android is an opensource operating system, you still don’t have full “root access” to do what you please on your phone. Back when the iPhone launched in 2007, the hardcore techies quickly realized the true potential of the device and the cruel software limitations that Apple had sealed it with. What became ‘jailbreaking’ on the iPhone was quickly translated to other platforms as well, and when the world saw the first Android back in 2008, the term “rooting” was born.[/quote]
So being rooted doesn’t mean something bad per se. As long as you do not grant root access to apps, which are insecure, no harm should be done.
As to your other problems, it sounds very much like a touchscreen failure. Please do the touchscreen test and report back! 