delete node from linked list (lang w/GC) -should deleted item 'next' be set to null
If you mean the next pointer of the node that was deleted, as far as I know it is normally not necessary to set the pointer to null.  Once the node is deleted, if the code is not buggy, then the code should not access the node after it is deleted, so the value of its next pointer should be irrelevant.  Sometimes some people do set the pointer to null, as a form of defensive programming (just in case the program is buggy and accesses that node after it was deleted).

I suggest that a useful exercise would be to ask your teachers why they teach yes or no.  Hearing their reasoning might be instructive and interesting!