I have been researching turbochargers and since they use outside air and exhaust to improve engine function couldn't that harm the engine? Or do I not understand the principle? Can't particules from the air that is gathered by the turbocharger harm the engine or is there a air filter in place that would stop this?
The only cars with turbocharges which do not have air filters are race cars. They do it this way so there is absolutely no restrictions on the intake tract. Race engines are routinely rebuilt as needed, so are not worried about small particulates entering the engine. Normal street driven vehicles will all have air filters on them, and as long as those air filters are replaced under normal maintenance, no harm from particulates will come during normal use.
A turbo sits behind an air filter on the intake circuit so it's no more likely to throw debris into your engine than a naturally aspirated car. Except maybe if the turbo sustains damage and a piece of the compressor wheel breaks off and gets sucked into a cylinder, but that won't happen unless the air filter fails first and lets something hard and heavy through.