Some comments

The fan should be placed well inside since the purpose is to reduce the humidity and odors.

As the bathroom will be used at night as well, the solar tube will not add to the lighting at night unless you intend to have a light in the tube.

Without knowing the light output of the various fixtures, it would be difficult to know whether there will be enough light.

The vanity is the most important area to light well in a bathroom - correct color representation, no shadowing of the face from the light position.