"I have never said" versus "I never said"

Sentence 1, while not strictly incorrect, sounds strange because it's normally the way you'd say that you have no experience with something. "I have never gone fishing," for example, is the only way you can say it as "I never go fishing" doesn't mean you have never once gone fishing but rather that it's extremely rare that you go fishing.

Your first example sounds a little odd. You are referring to one specific instance, so it would be more natural to say "I never said this." If you were referring to a number of cases, it would be natural to say "I have never said anything like this," or "I have never said anything of the sort."

The first sentence ('I have never said this') is a little unusual, but might be said to have the connotation "but I might say it at some time in the future". The second ('I never said this') is more usual and doesn't admit that possibility (though it doesn't deny it either -- that would require 'I would never say this').

Yes. Consider that:

I have said this.

I said this.

are both perfectly valid sentences. The first is in the perfect tense, the second in the simple past. Adding never doesn't change the validity of the tense forms. As others have pointed out, choosing the perfect tense is a little unusual and has some connotations you might not want.

"I have never said this" is in the present perfect tense and implies that at no time in the past have you ever made the utterance that "this" refers to. You might say this in response to an accusation that's shocking to some degree: "You told some of my friends that you hated me!", "No, you're wrong, I have never said that".

"I never said this" is in the simple past and implies that in one particular instance that is understood by the context you did not say what you're being accused of saying. "Did you tell Dale that you were going to wait for me on Tuesday?", "No, I never said that".

Note that in both constructions, it's probably more usual to use the demonstrative adjective "that" rather than "this" -- why? Because it seems to me that these phrases would most likely get used in response to a particular point by someone else said previously, and so you want to refer to that particular point.

If someone had a written phrase on paper, pushed it across the table to you, and then said "we believe that you made this statement", then you might look at it and say "No, I never said this" where "this" indicates "what's written on this paper".

In my opinion about I have said and I said it's about the situation when we say it. For the first is present perfect, the tenses means that you have done/haven't done something, but it is possible to do again. And for the second option is a simple past. Based on the meaning of past is something that we did, already happened and there's no impact which the first option has the impact.