To really understand this idea of photosynthesis, let’s look at the equation that defines it.

6CO₂ + 6H₂O ---> C₆H₁₂O₆ + 6O₂

This is saying that carbon dioxide and water combine, with the help of light energy, to form glucose and oxygen. If you decrease the amount of inputs (carbon dioxide and water) the whole process slows down because the plant has less incentive to do photosynthesis. Think about plants as factories that make a variety of different products. If you have less materials to make one of your products you’re not going to devote your machines, workers, and time into making that product when there are hundreds of other ways to spend your factory’s time and energy. All cells work like this and plants are no exception. Thank you for your question!

That depends on what is limiting the rate of photosynthesis in the first place. In a desert, this is usually water, so reducing the amount of water will reduce the amount of photosynthesis. For a plant with plenty of water and not growing in the shade, it's often carbon dioxide, so lowering that will reduce the rate of photosynthesis. For a fern living on the ground of a dense tropical forest, the limiting ingredient is often light, so lowering the amount of water or carbon dioxide won't do much.