Without actually causing any substantial damage to surrounding rock walls , and other natural formations , are we allowed to take rocks of any type from park land ? Also , are we allowed to dig for rocks as long as we refill the holes ?

Yeah not a good idea to. I have troubles with my kids wanting to. Look up leave no trace hiking. Leave What You Find Preserve the past: examine, but do not touch, cultural or historic structures and artifacts. Leave rocks, plants and other natural objects as you find them. Avoid introducing or transporting non-native species. Do not build structures, furniture, or dig trenches.

I am not sure, you should check with a park ranger. I I had to guess my answer would be no.