I think amount of lighting required for a space is typically determined by some kind of lumen calculation that I don't know enough about. Surely if your bathroom is that small you don't need another light, but hopefully someone on here can be more helpful :)

It is typically a good idea as tasks like shaving are often done in the shower. If you do install make sure it is a water tight recessed fixture.

I would recommend it. We just remodeled both of our bathrooms and added a light in the shower. Makes a world of difference - did not really realize how dark it was before!

I use the light in our shower every day. It is too dark without it.

I will add that we have a light over our totally glass enclosed shower that is never used.

Water and electricity don't mix. Depends where you are what is allowed.

A fan/light combination fixture, made for wet locations, is great for venting steam while providing light in the shower. Fantech makes great products that work very well and are super quiet.