In a Fullpage slider how can I make my image completely visible without cutting off parts from it or leaving empty space?

The answer to this topic's question is, that you can't. You could use  Stretch Fill mode, but that will make your image distorted, so it isn't really a good solution. In a Fullpage responsive slider you have to either cut off parts of your image or leave empty space next to it.

The definition of  Fullpage responsive mode is, that your slider will be exactly as big as the browser's screen is. This means your slider can have any size! For example it can be 1920*1080px on a FullHD monitor, but it also could be 320*568px on a phone. You have only one image, which has one size. That one image has to be adjusted to any screen sizes and for that you have to either cut off a part from it or to leave an empty space next to the image.

Just try to adjust this image to the two sizes under it:

This is the only solution to cover them without distorting the image:

and this is the only solution if you want to display the complete image without cutting off parts from it (there will be empty space):

If this is not acceptable for you, don't use Fullpage responsive mode, but use  Fullwidth instead, where your slider's size is what you give, so you could use the image's size as the slider size.