Warnings shown to anonymous users

You should check your web server configuration. The GD functions are disabled on the server; there is nothing that the module can do in such cases.
The module requires the GD functions to be enabled, but that is not happening on your server.

I checked the function that crop an image, and the functions you reported are used by that function. In this case, you cannot do too much; or those functions are enabled on the server, or you cannot use ImageAPI.

function imageapi_gd_image_crop(&$image, $x, $y, $width, $height) {
  $res = imageapi_gd_create_tmp($image, $width, $height);

  if (!imagecopyresampled($res, $image->resource, 0, 0, $x, $y, $width, $height, $width, $height)) {
    return FALSE;
  }

  // Destroy the original image and return the modified image.
  imagedestroy($image->resource);
  $image->resource = $res;
  $image->info['width'] = $width;
  $image->info['height'] = $height;
  return TRUE;
}

function imageapi_gd_create_tmp($image, $width, $height) {
  $res = imagecreatetruecolor($width, $height);

  if ($image->info['extension'] == 'gif') {
    // Grab transparent color index from image resource.
    $transparent = imagecolortransparent($image->resource);

    if ($transparent >= 0) {
      // The original must have a transparent color, allocate to the new image.
      $transparent_color = imagecolorsforindex($image->resource, $transparent);
      $transparent = imagecolorallocate($res, $transparent_color['red'], $transparent_color['green'], $transparent_color['blue']);

      // Flood with our new transparent color.
      imagefill($res, 0, 0, $transparent);
      imagecolortransparent($res, $transparent);
    }
  }
  elseif ($image->info['extension'] == 'png') {
    imagealphablending($res, FALSE);
    $transparency = imagecolorallocatealpha($res, 0, 0, 0, 127);
    imagefill($res, 0, 0, $transparency);
    imagealphablending($res, TRUE);
    imagesavealpha($res, TRUE);
  }
  else {
    imagefill($res, 0, 0, imagecolorallocate($res, 255, 255, 255));
  }

  return $res;
}