What is this permanent dark shadow on the bridge of my nose and how can I fix it? (photo)

Hard to tell from just this one image, but you seem to have very strong tip cartilages, and typically there is a shadow cast adjacent to the visible edges of strong tip cartilages. See the woman in the short video that I posted with this answer.You can click on the "Learn more" link, just below my response, or go here:
FacialSurgery.com/RealSelf/RealSelf_Svetlana93473.html
to see a morph I made of your photo, showing narrowing of the tip cartilages. I intentionally didn't color out the dark area, because I don't know that it would magically happen with changing the tip, unless it indeed is a shadow. But maybe the morph will help you analyze what's going on.

It is very difficult to be certain from the photographs you have provided but it does look as if you simply have very thin skin over the bridge over the bridge of your nose, which makes the structure of the nose look angular and irregular. If this is the case, this is something that can be corrected with several different rhinoplasty techniques but I would suggest that you seek a consultation with an experienced rhinoplasty specialist who has seen this problem before and who can illustrate the results of the surgery with previous cases. This is really the only way you can feel confident that you are in good hands and that you will get the result you want.

Hello,
Difficult to say from the photo. It could either be some pigment change in the skin or a shadow from an irregularity in the underlying bone / cartilage.
If it is in the skin, then some bleaching products might help.
If it is a small depression in the bone or cartilage, then fillers might be better.