It also scratches your paint job.
No it's not dangerous for a car but brake dust from pads asbestos fibers that can be hazardous to your health. Because asbestos is a good fiber for brake linings; it offers good strength, temperature, and chemical resistance, and is cheap compared to other materials that are used for the same purpose. Exposed fibers easily shred into thin needle like strands that can drift into the air and can be inhaled.
Hence the fibers lodge deep in the lungs where their sharp needle like strands become a source of irritation. To make matters worse, the human body cannot rid itself of these fibers because they are imperious to biochemical assault. So over time, exposure to them may result in lung disease or cancer.
No lectures on health hazards as you ask about your car. Dust will make it dirty but it is washable. Dust will harm your engine, but that is what air filters are there for. Make sure to change the filters when needed.
Not unless it gets in the engine. This is why you have an air filter.
If you are in dusty condition you need to check and possibly replace this daily.