Didachaic doctrines include those that are discerned via the correct exercise of the divine gift of logic.
For example, I view the following statements as logically a priori or unavoidable beliefs that are thus para-Scripture:
1. Truth or reality (your #1&4-7) exists. The classic expression of this belief was by Rene Descartes (d.1650): cogito ergo sum: “I think, therefore I am”. The OT says in Exo. 3:14 that God is “I am” (the essence of existence).
2. (Objective) reality is subjectively known by seekers (your #2&3, cf. Rodin’s sculpture; thinking is believing). David Hume (d. 1776) was a notable proponent of this opinion, and 2Cor. 5:7 expresses this truth by saying, “We live by faith, not by sight” (or proof, cf. 1Cor. 13:9&12 cited previously).
3. Reality is meaningful and communicable or able to be discussed rationally in fellowship with other truthseekers. As Isa. 1:18a (c.735 B.C.) says, “Come now, let us reason together.” Of course, because the discussion of reality uses language as the means, it is necessary to have a common language.
I just realized that whereas everyone (whether atheist or theist) agrees (at least implicitly) regarding a priori or unavoidable beliefs/logic or else they would not be sane, all Christians (whether any denomination) agree (at least implicitly) regarding God's requirement for salvation per the NT Gospel or else they would not be saved.