I'll assume--based on your expression "not supported by evidence"--that you are defining "faith" as belief without evidence.  Going on this assumption, I'll continue with the post.

Your three examples are not actually intrinsically wedded to atheism; you can be an atheist and deny all three.  For instance, all solipsists (a solipsist is one who believes that nothing exists except the self--hence a denial of the external world) are atheists.  Likewise, there's seemingly no prima facie inconsistency between an existential denial of God and that of one's self.  And finally, an atheist can easily deny both the existence of God and a natural causal order.

Perhaps you could say that a properly basic assumption to which all atheists must keep is that the nonexistence of God is logically possible, a proposition which perfect being theologians deny and which doesn't seem to be evidentially supported at all.  

As for your broad generalization of theism, without going into too much detail, I would disagree that those propositions are all evidentially unsupported.  But I think the bigger issue is that you seem to be misunderstanding what "faith" means to Christians.  It's not endorsing things that you know to be unjustified; it's trust in God, the person with whom you can be in fellowship and with whose existence you can sustain hope in the meaningfulness of your own life.  The reason to have faith, in fact, is because the evidence of God and his goodness, at least for certain Christians, is so compelling.  Similarly, I have faith in my parents, because they've shown themselves time and time again to be trustworthy.  In these terms, you really can't, as your wording indicates, put faith in a proposition, because propositions are not capable of a interpersonal relationships.

So the real question you should be raising is whose worldview is better supported, not simply whose axiomatic assumptions are greater in number.  Even if it was the case that my worldview as opposed to yours necessitated an axiom schema, it doesn't necessarily follow that my worldview is less justified than yours.   

Actually, it does.  Minimally, a prerequisite to not believing in something is that it's nonexistence is possible; if you didn't believe that the nonexistence of God was possible (i.e., if you believed God's nonexistence was impossible), then by logical necessity you'd have to believe that God exists.  Similarly, I couldn't lack belief in a unicorn unless I believed that it was logically possible for a unicorn to not exist.

The only way you could escape this corner is if you claimed that you merely believe in the epistemic possibility of God's nonexistence, i.e., "God could possibly not exist, as far as I know."

My interpretation of "faith" is supported in Reformed Theology doctrinal statements and is consistent with what's written in the Vatican Council.  

Here's a good read for you.  Also, some quotes:

"Faith in God then, is having the kind of trust and confidence in God and in Christ that leads you to commit your whole soul to Him as Saviour (Justifier, Cleanser, Healer, Deliverer) and Lord (Master, King).  In the general sense of the word, to have faith is to believe in something or someone, to fully trust, to be so confident that you base your actions on what you believe. To have faith is to be fully convinced of the truthfulness and reliability of that in which you believe (http://www.christian-faith.com/forjesus/faith-in-god)."

"(Pistis, fides). In the Old Testament, the Hebrew means essentially steadfastness, cf. Exodus 17:12, where it is used to describe the strengthening of Moses' hands; hence it comes to mean faithfulness, whether of God towards man (Deuteronomy 32:4) or of man towards God (Psalm 118:30). As signifying man's attitude towards God it means trustfulness or fiducia. It would, however, be illogical to conclude that the word cannot, and does not, mean belief or faith in the Old Testament for it is clear that we cannot put trust in a person's promises without previously assenting to or believing in that person's claim to such confidence. Hence even if it could be proved that the Hebrew does not in itself contain the notion of belief, it must necessarily presuppose it. But that the word does itself contain the notion of belief is clear from the use of the radical, which in the causative conjugation, or Hiph'il, means "to believe", e.g. Genesis 15:6, and Deuteronomy 1:32, in which latter passage the two meanings — viz. of believing and of trusting — are combined. That the noun itself often means faith or belief, is clear from Habakkuk 2:4, where the context demands it. The witness of the Septuagint is decisive; they render the verb by pisteuo, and the noun by pistis; and here again the two factors, faith and trust, are connoted by the same term. But that even in classical Greek pisteuo was used to signify believe, is clear from Euripides (Helene, 710), logois d'emoisi pisteuson tade, and that pistis could mean "belief" is shown by the same dramatist's theon d'ouketi pistis arage (Medea, 414; cf. Hipp., 1007). In the New Testament the meanings "to believe" and "belief", for pisteon and pistis, come to the fore; in Christ's speech, pistis frequently means "trust", but also "belief" (cf. Matthew 8:10). In Acts it is used objectively of the tenets of the Christians, but is often to be rendered"belief" (cf. 17:31; 20:21; 26:8). In Romans 14:23, it has the meaning of "conscience" — "all that is not of faith is sin" — but the Apostlerepeatedly uses it in the sense of "belief" (cf. Romans 4 and Galatians 3). How necessary it is to point this out will be evident to all who are familiar with modern theological literature; thus, when a writer in the "Hibbert Journal", Oct., 1907, says, "From one end of the Scripture to the other, faith is trust and only trust", it is hard to see how he would explain 1 Corinthians 13:13, and Hebrews 11:1. The truth is that many theological writers of the present day are given to very loose thinking, and in nothing is this so evident as in their treatment of faith. In the article just referred to we read: "Trust in God is faith, faith is belief, belief may mean creed, but creed is not equivalent to trust in God." A similar vagueness was especially noticeable in the "Do we believe?" controversy—one correspondent says—"We unbelievers, if we have lost faith, cling more closely to hope and — the greatest of these — charity" ("Do we believe?", p. 180, ed. W. L. Courtney, 1905). Non-Catholic writers have repudiated all idea of faith as an intellectual assent, and consequently they fail to realize that faith must necessarily result in a body of dogmatic beliefs. "How and by what influence", asks Harnack, "was the living faith transformed into the creed to be believed, the surrender to Christ into a philosophical Christology?" (quoted in Hibbert Journal, loc. cit.) (http://www.newadvent.org/cathen/05752c.htm)."

Hence, in Catholicism, it is inextricably tied to both trust and intellectual assent.  It's not simply anything which is believed without evidence.  

Now, what's more striking is your assertion that the core beliefs of Christianity have no supporting evidence, and that this lack of evidence constitutes a pillar of Christianity itself; however, neither proposition is endorsed by any theologian of whom I'm aware.  Even in St. Thomas's writings, the supposed "articles of faith" (so called because they cannot be known apart from Scripture) are rendered trustworthy insofar as they are revelatory products of an omniscient, perfect being; Aquinas is not saying that they have no evidence (indeed, they are plausibly true because of the nature of the truth bearer--a non-fallacious instance of appealing to authority) and should simply be believed out of personal preference.  The only thing close would be Kant's practical reason, in which he famously stated that practical reason demands an absence of a theoretical proof of God--but he was a philosopher, not a theologian. Otherwise, to say we have "faith" in God is to say that we trust God like we trust our parents or our spouses; it's not to say that we simply believe without evidence that God exists--that would be absurd.