Ketosis does not necessarily mean you are carb-depleted. It just means your carb levels are low enough that your body fuctions more efficiently on ketones.
If he's still growing at 18, he must have hit puberty very late. I think it's safe to say he's reached his adult height, and doesn't have to worry about having his growth stunted.
In theory, but only if you are really vigilent about only eating when you are hungry. If you tend to eat a certain amount at a certain time, then you need to watch the cals as well.
You can, but the keto headache is a minor thing that many people don't get. Don't go cold turkey on coffee, which is much more likely to cause a headache.