My brand new iPod Touch 4th Generation, just isn't functioning correctly.

Recently, I bought a brand new iPod 4th gen. Since, it has gone haywire and refuses to function correctly. It is 16 gb and operating on iOS 6.0.1. On many apps, especially games, it can get really laggy at times, for no discernable reason. I have very few apps installed, and a great internet connection, so I can't understand why that would occur. Also, Safari is absolutely useless. When opened, under any circumstances, It goes to a default white screen:

Then it can do NOTHING else. Upon further inspection, this seems to happen to a couple default apps. Such as:

-Calendar

-Maps

-Mail

After about 20 seconds of blankness, it then force-closes to the home screen. In addition, Game Center has become a pain in the butt; it just won't leave me alone. Anytime I try to open a game with internet capabilities (ie.Vector,The Sandbox, etc.), it pops up wanting me to sign in, yet it wont work. When I try to sign in, it never works the first time. I have to home-screen, then click the app again to open it up to the same page, before it even shows the keyboard, not to mention, at this screen, the keyboard is horizontal (landscape) while the rest of the screen is vertical (portrait). From this point, signing in does nothing, it will bring up the buffering circle and spin for about 10 minutes, before promptly force closing. I can't get out of that screen either, when it comes up asking for my log in, the cancel button becomes absolutely worthless, it does nothing. I've disabled Game Center's notification and changed it's capabilities, but it STILL comes up when I try to eneter a game. The only way around it is to completely TURN OFF my Wi-Fi. Thus rendering a lot of in-game content worthless. Lastly, sometimes the Game Center opens Safari, but since it doesn't do anything, I have no idea what to do. Home-screening does not work, as less than a second later, Safari opens again, and again, and again. The only way to stop this annoying cycle, is to completely SHUT-OFF my iPod.The iPod is only a little over a week old, and it ****** me off that I already want to put it down the disposal.