You should always turn on the vent hood to ensure you breathe as little of these elements as possible. A typical gas stove has a vent hood hovering above your burners.
Wipe the grates, surface, and burner caps with a damp cloth regularly. For a more thorough clean, soak the burner caps in warm water and clean with vinegar and baking soda paste.
Burners usually come in up to four sizes, with smaller burners meant for smaller pans. Using a wrong-sized burner or flame can over- or under-cook food.
Use the smallest burner for small pans, as too little food over too large of a flame can cause unwanted burning. More food calls for a larger burner, though there are exceptions.