Can you safely use a lower voltage on a DC motor?
1) Can I run a 12VDC motor on 6V or 7.5V without burning up the motor (or my home).


Yes, the fan will likely spin slower (that's fine for your needs) or it may not spin at all (in which case, you need a higher voltage).


  2) On an unrelated note: if I had a 9V 2A and a 9V 3.5A power supply, they'd act the same in regards to the motor, right? It just draws what it needs?


Yes. See here. A device will draw the current it requires and no more, regardless of the current rating of the motor.