The point was that dotted-list-p doesn't have anything to do with the "serialized form" (printed representation) of the list. Dotted lists are important because they are one of the two types of improper list, the other type being circular lists. Many Lisp functions work on proper lists.

Of course NIL is an ordinary symbol. It has roles, the same way other symbols have roles. Are you saying the symbol &BODY is not an ordinary symbol because it is a lambda list keyword? Are you saying the symbol T is not an ordinary symbol because type boolean is (member t nil)? Are you saying symbol * is not an ordinary symbol because it is a special variable bound by the REPL, it is used in declaration syntax, and also is the name of the product function? Are you saying MUMBLE:VAPORIZE is not an ordinary symbol because it names the most dangerous operation in the mumble library? They are all ordinary symbols, sometimes with unique roles. Because NIL was chosen to satisfy the role of the empty list, is it any wonder that type list is (or cons null), type null is (eql nil), LENGTH and ASSOC and other list functions can deal with it etc.? Of course not. That doesn't make NIL qua symbol any weirder than any other symbol that has particular roles in a given context.

There are many symbols in Common Lisp that you cannot DEFUN. See section 11.1.2.1.2 in the hyperspec. Since NIL names a constant variable but not a standardized function, macro, or special operator, you can bind it to a function lexically using FLET or LABELS.

Once again, NIL is not a cons, it is an atomic symbol that also represents the empty list, so it's no wonder that LISTP returns true and CONSP returns false. CAR and CDR take lists (again see their entries in the CLHS) so it's no wonder that they can work with it. RPLACA and RPLACD take conses only so it's no wonder that they don't. At the risk of stating the obvious (again and again) the type null is (eql nil) so it's no wonder that NULL returns T for it. That operators treat a symbol specially does not make a symbol weird. It merely means that it serves a particular role. Any symbol can take any number of roles within a program. That doesn't make the symbol weird. I will repeat once more, because I've a feeling you didn't get this. It doesn't make a symbol weird.

It is a basic matter, definitely. I learned all this stuff about conses, atoms, symbols, lists, etc. very early on, as baby Lisper. I don't know why someone who spent 35 years programming Lisp should have trouble understanding all this, and has to keep bringing up new irrelevant/incorrect claims instead of just opening a beginner's Lisp book and re-reading the first chapter or two, where they talk about all this stuff.