[3-3] I used a destructive function (e.g. DELETE, SORT), but it didn't seem to work. Why?

I assume you mean that it didn't seem to modify the original list.  There
are several possible reasons for this.  First, many destructive functions
are not *required* to modify their input argument, merely *allowed* to; in
some cases, the implementation may determine that it is more efficient to
construct a new result than to modify the original (this may happen in Lisp
systems that use "CDR coding", where RPLACD may have to turn a CDR-NEXT or
CDR-NIL cell into a CDR-NORMAL cell), or the implementor may simply not
have gotten around to implementing the destructive version in a truly
destructive manner.  Another possibility is that the nature of the change
that was made involves removing elements from the front of a list; in this
case, the function can simply return the appropriate tail of the list,
without actually modifying the list. And example of this is:
   (setq *a* (list 3 2 1))
   (delete 3 *a*) => (2 1)
   *a* => (3 2 1)

Similarly, when one sorts a list, SORT may destructively rearrange the
pointers (cons cells) that make up the list. SORT then returns the cons
cell that now heads the list; the original cons cell could be anywhere in
the list. The value of any variable that contained the original head of the
list hasn't changed, but the contents of that cons cell have changed
because SORT is a destructive function:

   (setq *a* (list 2 1 3))
   (sort *a* #'<) => (1 2 3)
   *a* => (2 3)     

In both cases, the remedy is the same: store the result of the
function back into the place whence the original value came, e.g.

   (setq *a* (delete 3 *a*))
   *a* => (2 1)

Why don't the destructive functions do this automatically?  Recall
that they are just ordinary functions, and all Lisp functions are
called by value. They see the value of the argument, not the argument
itself. Therefore, these functions do not know where the lists they
are given came from; they are simply passed the cons cell that
represents the head of the list. Their only obligation is to return
the new cons cell that represents the head of the list. Thus
"destructive" just means that the function may munge the list by
modifying the pointers in the cars and cdrs of the list's cons cells.
This can be more efficient, if one doesn't care whether the original
list gets trashed or not.

One thing to be careful about when doing this (storing the result back
into the original location) is that the original list might be
referenced from multiple places, and all of these places may need to
be updated.  For instance:

   (setq *a* (list 3 2 1))
   (setq *b* *a*)
   (setq *a* (delete 3 *a*))
   *a* => (2 1)
   *b* => (3 2 1) ; *B* doesn't "see" the change
   (setq *a* (delete 1 *a*))
   *a* => (2)
   *b* => (3 2) ; *B* sees the change this time, though

One may argue that destructive functions could do what you expect by
rearranging the CARs of the list, shifting things up if the first element
is being deleted, as they are likely to do if the argument is a vector
rather than a list.  In many cases they could do this, although it would
clearly be slower.  However, there is one case where this is not possible:
when the argument or value is NIL, and the value or argument, respectively,
is not.  It's not possible to transform the object referenced from the
original cell from one data type to another, so the result must be stored
back.  Here are some examples:

   (setq *a* (list 3 2 1))
   (delete-if #'numberp *a*) => NIL
   *a* => (3 2 1)
   (setq *a* nil *b* '(1 2 3))
   (nconc *a* *b*) => (1 2 3)
   *a* => NIL

The names of most destructive functions (except for sort, delete,
rplaca, rplacd, and setf of accessor functions) have the prefix N.

In summary, the two common problems to watch out for when using
destructive functions are:

   1. Forgetting to store the result back. Even though the list
      is modified in place, it is still necessary to store the
      result of the function back into the original location, e.g.,
           (setq foo (delete 'x foo))

      If the original list was stored in multiple places, you may
      need to store it back in all of them, e.g.
           (setq bar foo)
           (setq foo (delete 'x foo))
           (setq bar foo)

   2. Sharing structure that gets modified. If it is important
      to preserve the shared structure, then you should either
      use a nondestructive operation or copy the structure first
      using COPY-LIST or COPY-TREE.
           (setq bar (cdr foo))
           (setq foo (sort foo #'<))
           ;;; now it's not safe to use BAR

Note that even nondestructive functions, such as REMOVE, and UNION,
can return a result which shares structure with an argument. 
Nondestructive functions don't necessarily copy their arguments; they
just don't modify them.
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