Yes.

Clean dust : look for HEPA filter
Fresh air : no such thing. Air purifiers only filter stuff from the air in the room. It cannot generate new air. For fresh air, either open a window or add an exhaust fan installed in reverse blowing fresh air in. But the air will only be as fresh as the air outside your window. If you're living next to a busy road, it wouldn't be very nice. No purifier can remove CO, NO, or whatever poison pumped out by vehicle exhausts. They only remove particulate matter, not gases. The only way to get fresh air is to live so high that you're actually above the city smog (which my own house used to be but isn't anymore, 12km from KL city center, and atop a small hill) or you relocate to a geographic position far enough in the countryside that you have fresh air outside your window.