Back Carb \ Sweetening

I am looking to make a sweet carbonated cider.

I will be adding a non fermentable sugar ( Xylitol ) to sweeten. How much should I add or consider adding to a 4g batch? I want it to be semi sweet.

With carbonation, I would like to skip cold crashing/pasteurizing. How much corn sugar should I add to carbonate 4g without having to do either?
http://www.tastybrew.com/calculators/priming.html How accurate is this calculator?

If I do this correctly, I can have the sweeteneed and carbonated cider without cold crashing / pasteurizing.

You certainly can! I can't help with how much Xylitol, but those calculators work great. Don't carb above 3 volumes of CO2 in standard glass bottles, and make sure you boil the sugar in a little water then put it in your bottling bucket before racking. If you need general bottling tips, check out the stickies in the "bottling/kegging" subforum.

After the fermentation does the cider have about 1 residual volume meaning I can only add 2 volumes, or can I add three volumes to it?

The bottles can hold about 4-5 volumes from what I have read but I only want to do about 2 volumes unless anyone else has any recommendations on what a cider should have.

This will be my first bottling as my last batch went to wine then vinegar.

Regarding carb level, it's completely up to you. Some people enjoy more carbonation in a cider, some people less. If you're using thick-walled glass bottles or plastic bottles, you can probably do above 3 volumes, but otherwise I'd keep 3 as your max. You don't want the bottles to explode! And that's the total carbonation, including residual post-fermentation CO2.

If you input "3 volumes" into that calculator you linked, it will give you the appropriate amount of sugar to get a total of 3 volumes including the residual CO2.

the carb volume is easy -- the tricky part is going to be finding how much xylitol to add. most people recommend adding a measured amount to, say, half a pint until it is at the desired sweetness. then scale up from there.

from what i know, you'll probably want in the neighborhood of 2/3 cup (125 grams)

let us know how much xylitol you add and how it turns out. there aren't a lot of field reports out there.