Palm kernel flakes can be substituted for coconut oil as they both add high suds properties to soap. I would try lard or tallow as a substitute for palm.
No, palm kernel flakes would be used as a substitute for coconut oil. Lard or tallow would be a substitute for palm, or soy wax and butters if you are looking for vegan friendly.
Shea butter & cocoa butter are also a good sub for palm.
This subject has been discussed many times. If you go to the menu at the top of this page, on the far right you will see a "magnifying glass + Search". Enter "Palm Free" in the search box and tick "Titles only" to find more information on this subject.