Additional power draw on the accessory circuit places increased load on the alternator which in turn causes the engine to run a little harder than it otherwise would. Thus burning a little extra fuel.
They produce based on current draw, but have a maximum output, usually around 60-85a for and older car, to 120-240a at 14.4vdc for a newer car or truck. There is no permanant magnet, so the coils require power to generate power. Its quite interesting.
Further to this the 12V battery effectively acts as a big capacitor while the car is running, to smooth out the power that is available.
I found this out the hard way a couple of years ago. My 12V was dead, yet I managed to jump start the car and get it running. I thought it would be ok to drive to get a new battery, as long as I kept the engine running high enough. After a couple of km the dashboard lights started to dim, so I tried reving it as high as I could, but the battery wasn't able to buffer the power and supply the ignition system, so the engine stopped. It was rush hour and I was in the middle lane, so it wasn't a particularly fun wait for the tow truck.