The breadboard is definitely wrong. The breadboard doesn't have good connectection and certainly not for such current !
Do you use 12V DC ? Not AC I hope.
Do you want to dim the lights with PWM, or only switching them on and off ?
The power mosfet is only 17 or 22A. Halogen lamps can be very nasty for the very high peak current during power on. You might want use a mosfet that can handle more.