Putting a heat lamp in a coop CAN be a fire hazard, but no more than a heat lamp in a house. If installed properly, there is no more risk. I used three in my coop, hung at least 18 inches from the floor with double safety (two chains so if one broke the other would hold). If attached securely and correctly, they are fine. Obviously, don't attach them with clips or close to wood or bedding.
Birds can see the red spectrum (unlike some other animals) so the coop will not get totally dark, but the chickens will get used to it. I used florescent lights on timers to simulate daylight and egg production slowed, but did not completely stop.
it is important to add that in my area, temperatures get down to below zero. Last night (October 10/11) was 35 degrees already. I have mostly Serama, which are considered a lighter feathered bird, so this is why I heat. If I had a larger bodied/feathered bird, I wouldn't bother.