We used a plastic bottle that Pizza Face and Billy gets hit with. Pizza Face then does a forward summersault and plops flat on the floor. The extra action detracts from the fact that the bottle doesn't break. 

We didn't light the closet. There was enough glow from the stage lights.

Our Billy did change his voice -- but that should be a director's call. It may be funnier if your Billy uses his normal voice. The screwball nature of this farce gives you licence to do what's funny, not what's "believable."

Both my actors played football in college so tossing the baby became a great shtick.

An extra touch: We used a stereo amplifier for the baby crying sound effect and panned the sound to follow the action on stage. In another production I saw, they used a tape player hidden on the food cart, but clicking the on and off controls was too obvious and the mechanical noises of the tape player too distracting.