Yep. You will need a regulated 12V wall wart or something. The voltage range on the sensor is 9.5V to 16V.
Power going into the sensor should not affect the FEZ in any way, assuming the sensor just connects and disconnects a relay. The FEZ and the sensor are on two completely different circuits.
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3) How do i wire this detector to Mini, like red/white go to where in mini, N.C wires go to where in Mini?[/quote]
You’ll wire it up like a switch, because that’s what it is. You will also need a pulldown resistor to pull the pin to ground when the relay is disconnected. Otherwise, the pin will be floating, which is BAD.
There is also an Arduino tutorial here that shows you how to wire up a switch. This is what you need: Arduino Tutorial - Lesson 5
If you google "Arduino switch you will also get plenty of results. A relay is exactly like a switch except for it it is triggered by an actuator, not a human finger
I wasn’t all that far away from your offices last week while I was in Wisconsin. It would have only been around a 2 hour hop across Lake Michigan, but that’s still 4+ hours of aircraft fuel.