Carbs are not essential to life, but if by health you mean the optimal functioning of your body and mind, they may be essential for you. The optimum level of carbs in the diet varies between individuals, and is found by trial and error. Your optimum carb intake may be 0, or 50gm/day, or 100, or 150, or more. It depends on your individual metabolism, diet and activity level. Also, your optimum carbs may vary over time.
No. Your body doesn't need carbohydrate it needs nutrients, whether or not the foods out there in the world containing these nutrients also contains carbohydrate/protein/fat is arbitrary.* (Though there are some essential proteins and essential fats there are no essential carbohydrates).
That said there may be some advantages to having some carbohydrates, sufficient to limit to how long or how deep you're in ketosis, as in the long run this may be more stressful for the body than staying just out of ketosis. (Discussed here: http://high-fat-nutrition.blogspot.com/2009/11/brief-discussion-of-ketosis.html)
*Though as it happens your best bet for micronutrients in general will be meat and low carb veg, there's nothing you can't get from those that you can get from grains or starches.
Optimal health may depend on exercising intensely from time to time. Some forms of intense exercise require higher muscle glycogen stores than can be reasonably obtained with a low carbohydrate intake. One can adapt to a low carbohydrate intake for very short or very long athletic events, but for high intensity aerobic events (a 20k run or 40k bicycle time trial, for example) there is no way around the well-established biochemical fact that metabolizing carbohydrate requires less oxygen per unit of energy produced than metabolizing fats or proteins. For most well-trained people, getting enough oxygen to the working muscles is the limiter in these events. Training in a glycogen depleted state may lead to helpful adaptations, but competing without ample glycogen stores will lead to sub-optimal performance.
Carbs are non-essential to good health. In fact the only good reason I can see to actively consume carbs are if you are an athlete who performs anaerobic activity. And even then only immediately before and after the activity...though I'm sure others will disagree with this. I don't carb load but I don't do HIT either...I'm more of the long walk in the sunset type.
I was a member of the Zero Carb community for a couple of months and during that time I fully embraced the ZC lifestyle. Its not for everyone, and infact it wasn't for me, though many people find peace and comfort in the simplicity of eating only meat.
I truly enjoy vegetables and participating in "gathering" activities for seasonal fruit (pick-ur-own berries). And you'll have to pry the whipping cream out of my cold dead hands...lol.
The reason why we eat these carbs is because we're acclimated to do so by our family traditions. As a result of my experiences, I no longer force my children to eat their vegetables...much to the consternation of their father ;-). If you look at the traditional diets of HG societies thoughout the world, you will notice a wide variety of the amounts of carbs consumed...from near zero(inuit) to very high(kitavan). And each of them is a healthful diet...because the food is "whole".
No. Carbohydrates contain no nutrients that you couldn't obtain otherwise. It is true that your body needs some glucose but it can produce that through glucogenesis without any carbohydrates.