Q 2) Does this unity consist only in the words and acts of Jesus Himself, or also in the witness of the NT authors?
We do not know what Barth would say to this, and so will endeavour to think out the question further for ourselves.
"At its climax, where exegesis must pass into original thought, a dogmatics which limits itself to being merely a Biblical exegesis, inevitably becomes the pious word of the man of today, to qualify which is, however, its very business. All too often, material Biblicism has in fact made an arbitrary 'Sic volo, sic jubeo,' the first and last word of the dogmatist who adheres strictly to the Biblical text, and has caused historical, psychological and speculative thought to reign unhindered as though dogmatics were non-Biblical; and dogmatics, qua critical discipline, has thus neglected its very task. It should not be forgotten that whereas material Biblicism is quite a modern phenomenon, only too closely related to the psychology of religion, the Biblicism of Reformed dogmatics, for example Calvin's, is clearly distinguished from mere exegesis, and in distinction from preaching and exegesis invites us to a Scriptural attitude of thought which is formal Biblicism" (439).