Is it safe to use the HPA5100 with an extension cord, and are there other important safety precautions?

No, you should not use the air purifier with an extension cord or power strip — locate it near the outlet and plug it directly in. Additional safety precautions include never using the unit outdoors, never blocking the air outlets or intakes, always using the unit in its upright position, and keeping it out of reach of children and pets. (Page 2)