For your first point, how? I honestly do not know where your confusion is. What statement is contradicting which other statement? I am stating that being uncertain if a god exists or does not exists falls within atheism as atheism is being unconvinced that a god exists.
In other words, I am pointing out that what some people claim the definition of agnostic to be is in fact atheism i.e. there isn't a middle ground (the law of the excluded middle). You either believe god exists or you do not believe god exists (a true dichotomy) and saying "I don't know" is still atheism as it is being unconvinced. They are saying "I do not know" to the question of "Does god exist" NOT to "Do you know god exists" which is why it is a belief claim not a knowledge claim, it's just that the expression includes the word "know" in it.
If your answer is "I do not know" to the question of "Do you know god exists" then that is agnosticism. If I made this more confusing I apologize. And yes, anti-theism is still atheism but atheism is not anti-theism. So it is correct to say that an anti-theist is an atheist but the reverse isn't true. Anti-theists actively proclaim that god does not exist (and therefore they obviously are unconvinced that god exists) while an atheist is simply someone who is unconvinced of god existing. An oak is a tree but not all trees are oaks type of situation.
No progress can be made in these discussions until both parties are using clear definitions of words that easily allow one to say whether any given thing is included in the definition or excluded. It's not even essential that that both arties use the same definition as long as they both understand what the other means. I define words in the way that makes them most useful to me. For example, for me, the only definition of a religion I use includes gods and supernaturalism. You don't need to use the word this way, but if you understand that that is what I mean when I use the word, you can understand why I don't call secular humanism a religion, even if you do.
On the other hand if we don't do at least this, we're merely arguing past one another using different definitions that cause us to keep saying, "Well that's not what an atheist is" as you are doing here. No, atheism and agnosticism can be defined in such a way that one can be both, neither, or either one without the other. For me, atheism is merely the lack of a god belief, and agnosticism is saying that we do not know and cannot decide if god's exist. If one does this, all of the confusion above disappears. You don't have to use those words that way, but if you know that I do, you understand me when I say that I am an agnostic atheist, and it's clear that I am. There is nothing to argue about. I'm telling you that I don't believe in any gods, but that I do not claim that they cannot exist, which is my position exactly. To start using different definitions to rebut me is pointless. There is nothing to rebut. You ought to agree that if I use those words those ways, and these are positions on belief in gods and knowledge about gods, then I fit into my own definition.
A point of illustration. I'm a avid contract bridge enthusiast. There are two schools of thought on whether a 1NT opening bid is appropriate holding 5 hearts or spades (5-card majors). I play that I don't open 1NT with a 5-card major. Occasionally, I am playing with a partner who does. No problem as long as we have been clear to one another what this bid means when each makes it. Only if we use different definitions of a proper 1NT opener and don't clarify and acknowledge those differences is there a communications problem.
In my opinion, it's this lack of clarity regarding definitions that underlies all of these semantic debates. When you say, "I am stating that being uncertain if a god exists or does not exists falls within atheism as atheism is being unconvinced that a god exists." Well, not for me. If you can understand that, even if you don't like to use the words the way I do, we can communicate. If you can't or stubbornly insist that your usage should apply to as well, nothing productive can come out of further discussion. And showing me dictionaries with definitions that vary from mine as if that compels me to use those words that way is meaningless to me.
Whenever you talk about no god concept do u mean the lack of belief in god? I know athiest talk about a mental state rather than a knowledge one.
Yes, no god concept means no believe in a god, the sine qua non of atheism as I use the word. That unbelief is both necessary and sufficient in the definition, meaning it need be there to call someone an atheist, but nothing more, especially any statement on whether gods can be known to exist or not. Either answer is an atheist if there is no belief in a god.
If by mental state, you mean the presence or absence of a belief in gods, then yes, atheism is the mental state of a person who answers no the question whether they believe in any gods.