How do you modify recipe to cook in crockpot

To answer your specific questions about modifying or adapting this recipe for BBQ pulled pork, to use a CrockPot / slow cooker instead of the oven:

I would reduce the liquid by about a cup. If there is too much liquid after the meat is fully cooked, you can reduce it if necessary in a saucepan on the stove. You need enough liquid to create plenty of steam to cook the meat.

How long to cook this? On low, it will take quite a while - 12 hours at a minimum; on high, it will be more like 4 to 6. You can speed it up a bit by cutting the meat into four or five large chunks before putting it into the pot. I would also brown those chunks in a heavy pot on the stove, to improve the flavor of the dish - but that will also heat the meat, which will reduce the cooking time overall.

Should you add the barbecue sauce at the beginning? I would probably add a bit of it to the apple juice, to get the flavors into the meat, but I would wait to add the rest of it until the end, as suggested in the recipe.

Here is a helpful article on modifying for slow cooker use recipes for braising in the oven.
https://food52.com/blog/8662-how-to-adapt-a-recipe-to-a-slow-cooker ;o)