Learn English – Nothing / Anything

Your b) versions are ungrammatical in standard use because they employ double negatives.

I cannot say nothing else would only be used with emphasis on the 'nothing' to assert that you do in fact have something else to say.

I cannot say anything else would require a just before anything and would emphasize anything to assert that the something else you have to say isn't just anything you say to be part of the conversation but is highly specific or relevant to the topic at hand.

If you want to use 'nothing' in these contexts you must delete the 'not':

I can say nothing else because I noticed nothing else.

Even in non-standard use, where double negatives are sometimes employed for additional emphasis, you are unlikely to encounter them in the forms you offer; the negated verbs would be contracted:

I can't say nothin else cause I di'n't see nothin else.

In my part of the country you wouldn't say even that; you'd say:

I can't say nothin else cause I ain't seen nothin else.

1. It's cold today.
2. It's easy to do.
3. It's nothing.

For your example #1: It's cold today.

The term I use for that "it" (in #1) is dummy pronoun, and it is a dummy pronoun that realizes subject function.

Evidence that shows "it" to be a subject is: "Has it been cold today?" (subject-auxiliary inversion). The "it" underwent inversion with the auxiliary verb, and so, it probably is the subject.

Evidence that shows "it" to be a pronoun: "It is cold today, isn't it?" (interrogative tag question). Only pronouns can be subjects of the tag question.

As for your other examples (#2 and #3), er, they might be regular pronouns (that is, they are not dummies). You might want to surround them with a context, and then, you might see that the "it" actually does have an antecedent.