Cooking with hard cider, when reduced to almost gone while braising, do the calories/carbs change? Get lower?

The amount of calories and alcohol remaining in your dish will depend on the proof and volume of the alcoholic product you began with. It will take longer to burn off the alcohol from something like vodka - at around 40 % ABV, than it will hard cider- which is around 6% ABV. Calorie contribution also depends on how much alcohol remains- and it is about 7 calories per gram of alcohol. So if most of the alcohol evaporates, the calories it contributes will evaporate as well- to the point of becoming negligible.