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1) The number of images that you use to make the calibration matrix is important. Try to make at least 10 image from chessboard in different situation. Also be carefull about the condition of photographing, they should be the same, specially "Focal Lengths" and "Resolution".
It seems that problem "2" and "3" will be solved if you manage problem number one.
I strongly suggest you to read and implement the camera calibration part from Learning OpenCV book.
