Does the type of container affect the evaporation?
Evaporation only happens at the surface. So a wider container that allows for a greater surface to be in contact with air, the faster the evaporation.
Yes and no. The shape can affect how efficiently the water is being heated and how efficiently the evaporated water can escape a vessel. An almost completely sealed water container will show very little signs of evaporation because any water that evaporates will soon condense back into the container. The evaporation is still happening, it's just not as observable or relevant because the evaporation cannot leave the system efficiently.
While water its self doesn't come in different colors things like the color of the container or surface it is on and any dyes in the water would affect the rate of evaporation. Water on a black surface would evaporate faster than one on a white surface. likewise if you were to dye the water black the dye would absorb more energy and heat the water faster resulting in faster evaporation.
The exposed surface area of the water will affect the rate of evaporation since it controls how many particles can escape at once and the odds of a particle escaping into atmosphere rather than simply bumping into another particle and changing direction. That means if you have two containers of equal volume, the wider one will evaporate marginally faster. I'm not sure what you mean by what should the not do.