To sit at the chef's counter, which is referred to as 'The Cooking Place', just request it when you check in at the podium. If you are planning on dining at peak times it might be best to call the podium or stop by around 5:30 and make your request then.
As for service, the menu is the same. However, that particular station can get very busy, since a server might have a number of different parties at the counter in addition to their regular tables.
For children, it's usually a lot of fun for them to watch the food being prepared. I would be concerned about little ones and toddlers, since the seats are more like bar stools; they're high and they don't have arms. If they like to wiggle around, a normal table might be a safer place.