Partial answer, too long for a comment:
Rule #1: Gimp works with pixels, because the real data in your image is in the pixels. Everything else can be set/reset easily. However, modifications to pixels are final. With this in mind:
When you load a PDF the default print definition is 100 PPI. This is usually too low for printing; you can set the print definition to 300 PPI when opening the PDF, and aim for a 1200×1800 px image to be printed in 4"×6" format.
The image as displayed by Gimp on your screen is not the size of the printed image. By default, Gimp maps one pixel in the image to one pixel on the screen (aka "dot for dot" view). So the image is displayed with the definition of your screen and not with the "print definition" set in the image. This can be toggled with View → Dot for dot.
When you copy to a new image, Gimp copies pixels. But the print definition is the one of the target image. You can reset the print definition of an image using Image → Print size, keeping in mind that this doesn't change the size in pixels, only how big it is printed (and displayed if not using dot for dot).
There are are several way to rotate an image (or parts of it). The Rotate tool requires to “commit” the rotation when you are happy with what the preview shows (otherwise it resets the rotation when you switch to something else). But in your case you likely want one of the Image → Transform → Rotate 90° CW|CCW actions.