Questions...

Could you provide us with some more info?

What phone do you have?
What version of android do you have on it? Goto settings - about, phone to find out.

Maybe then a Guide/Mod can put this in the appropriate forum, where others users with the same phone can help provide better answers.

You can stop internet traffic on your phone by turning data off in the wifi settings, or by long pressing the power button and selecting the data option.

To move/erase a widget, long press on it, until the phone vibrates, or until the widget gets bigger, then without removing your finger from the screen, drag the widget to where you want it, or to the bin, the bin area will turn red, then release your finger, and it will be gone.

You can add widgets/shortcuts to your home screen by long pressing a clear area of your home screen and following the menu that appears. Experiment, see what other things you can add.