The apple juice is recommended to soften the liver/gall stones prior to the flush.
This is my first MC, but apple juice would probably be ok to use coming off the fast. I plan to filter mine at first, to make it easier to digest. I'm still going to do the orange juice after the Liver Flush to make sure my digestion is ready before I chow down my first salad.
Ropes is a term used for the long pieces of bowel matter that cleans out with the P&B shakes. They are rubbery and often have kinks, etc. because they have been inside your intestines for a while. I haven't heard "cords" before, but sounds like the same thing???
Hope that helps. Best wishes on your journey to health!