There is a simple reason for our disagreement. You do not believe that reason is (possible/efficacious/valid). I do, though this belief is not based on faith. The argument for why reason is valid is given by Ayn Rand. You are not familiar enough with her argument to defeat or disprove it. Anyway, my response to your specific claims follows. I respect your wish to end the conversation, so I don't mind if you don't respond.
The mere fact that something is necessary for knowledge does not mean that it is true because it has not been established that we are able to know. Nor is it established that we are able to experience.
It has been established. All the evidence supports that we are able to know and that we experience. I don't know what you mean when you say that this has not been established. No, we are not omniscient... but, for example, we could not build computers (for example) if we were not able to "know".
As you can see, there are far more fundamental axioms than the one that the Objectivists posit and even these can be reduced further.
No, I honestly can't see that. What is a more fundamental axiom than those of Objectivism?
The choice of which first principles to choose are by no means an objective one, but instead a pragmatic one.
No, they are objective. They are the only primary concepts that are implicit in and fundamental to all knowledge. Can you name some other concept for which this is the case? They are also self-evident, though they are not the only concepts for which this is the case. (By the way, self-evident does not mean "obvious".)
You're establishing a useless distinction: If you told my about a Faerie you saw one day and I believed you, then my belief would not be without evidence; your testimony counts as evidence. Doubtless, you consider that to be insufficient evidence, but it is evidence non-the-less. You are positing a 'faith' that no one, religious or not, holds.
My report of seeing a fairy could count as evidence if you consider me a credible source and if the properties I ascribe to it are not contradictory to other evidence. Religious faith does not have evidence to support it, because the Bible and religious leaders are not credible enough to outweigh the evidence that suggests that miracles and so forth are impossible. In fact, if you ask a religious person to justify their belief in their religion, ultimately, they will cite faith as the source of their belief. I am positing a "faith" that all religious people hold.
Not to put to fine a point on it, but what you seem to mean is that faith, as you define it, is a belief based in something other than Objectivism, which is also a useless (and subtly religious) definition.
Objectivism is not "subtly religious" because it is based on reason. If you can show Objectivism to be in error, please publish a paper showing the error. It is clear from this discussion that you do not understand Objectivism.