What is the ruling on shaving or trimming the beard, or removing it with Photoshop in pictures, out of necessity or otherwise, for reasons of travel to a country where one fears for a bearded person?

It is not permissible to shave the beard except out of necessity. It is permissible to trim it by taking what is less than a handful if there is a need, or by taking what exceeds a handful. If the purpose can be achieved by removing the beard from the picture only without shaving it, then there is no need to trim it.