How do I stop the image from moving off screen in full screen mode.

I turned off Settings > Tools > OVERSCROLL

If you crop in Tab of Floating window and you use fit in window and set a crop selection with the marque tool the image will not pan. However you will not be able to rotate the selection and crop and straighten at once.  The Crop tool is a good tool but Personally I do not use the crop tool myself.  l for I do not like how it works and do not particularly need some of the features the crop tool provides like retaining what is cropped or resampling what is cropped.  I guess I'm simple minded I do one thing at a time.  I also use smart object layers to resize and mask or clip off what I do not want.  When I do crop I normally do it in two steps,  Marque Select then image  crop. Call me simple it you wish too. To fine tune a crop you can always views actual size after setting the marque tool and use Transform selection to fine tune it.