What did Protestant reformers think about the date and authorship of the New Testament?

There are two things to clear up. And then, based on that clarification, make a comment.

CLARIFICATION

First, until the founding figure of doubting scripture wrote about 1750, most likely everyone believed the historical idea that the New Testament was written between 45 and 105 CE. This change in attitude toward the traditional dating postdates the Reformation that took place from 1517 to 1648.

So, there’s virtually no doubt that the Reformers agreed with the historical teaching that the New Testament was penned between the times of the first and last apostles to die (James and John sons of thunder).

Second, no one would seriously dispute that the apostles spoke first and then wrote. Irenaeus circa 180 CE for example says this (first quote below). Scripture itself says it here and here among many other places!

REAL ISSUE

The real dispute in Irenaeus’ time that over centuries would nonetheless develop and later lead to the Reformation was the conflicting idea that the apostles spoke orally something that was necessary to one’s salvation, but failed to write it down. In other words, everyone agreed the apostles spoke and then wrote. The dividing dispute was whether what they spoke had a bearing on truth found not only in scripture (necessitating a teaching mechanism), but also apart from scripture (requiring another source of truth). Irenaeus puts it this way;

1. When, however, they [the heretics] are confuted from the Scriptures, they turn round and accuse these same Scriptures, as if they were not correct, nor of authority, and [assert] that they are ambiguous, and that the truth cannot be extracted from them by those who are ignorant of tradition. For [they allege] that the truth was not delivered by means of written documents, but vivâ voce: wherefore also Paul declared, “But we speak wisdom among those that are perfect, but not the wisdom of this world.” And this wisdom each one of them alleges to be the fiction of his own inventing, forsooth; so that, according to their idea, the truth properly resides at one time in Valentinus, at another in Marcion, at another in Cerinthus, then afterwards in Basilides, or has even been indifferently in any other opponent, who could speak nothing pertaining to salvation. For every one of these men, being altogether of a perverse disposition, depraving the system of truth, is not ashamed to preach himself. AH Book III Chapter II P1

For Irenaeus, the “system of truth” is found in nothing other than preaching scripture.

Finally, many misunderstand Irenaeus’ support of tradition, as if, again, that tradition was not already known via scripture and faithful men. Irenaeus is very keen on the idea of faithful men handing down faithfully (identically) that which scripture tells, that which apostles knowingly said. That same tradition could once be found identically in the church, whether at Rome, Smyrna, Ephesus, or elsewhere. Again, here is Irenaeus;

2. But, again, when we refer them to that tradition which originates from the apostles, [and] which is preserved by means of the succession of presbyters in the Churches, they object to tradition, saying that they themselves are wiser not merely than the presbyters, but even than the apostles, because they have discovered the unadulterated truth. AH, Book III, Chapter II, P2

Tradition must originate from apostles (written scripture) and is maintained, not changed, added to, or subtracted from, by means of a succession of faithful elders in the churches. Those who object to this system do so on the basis, again, that the apostles left something out of their writings that others discover.

CONCLUSION

So, the Reformers would have agreed with the historical view that the apostles spoke first from 30 CE to about 105 CE and then wrote from about 45 CE to about 105 CE.

Further, the Reformers would be agreeing with the historical view that the apostles did not leave out anything necessary for one’s salvation from their writings that we all call the New Testament.

There never was any argument between the Reformers and the Catholic church regarding the canon of scripture, just as they never had any difference of belief about the Trinity doctrine. Going back to Martin Luther, here is a quote from a historian:

The Bible for him was not strictly identical with the Word of God. God's Word is the work of redemption in Christ which became concrete in Scripture as God in Christ became incarnate in the flesh; and as Christ by the incarnation was not denuded of human characteristics, so the Scripture as the medium of the Word was not divested of human limitations." (Here I Stand, p 331, Roland Bainton, Lion 1988)

He goes on to deal with Luther's translation of the New Testament into German, published in 1522. Although Luther had "a hierarchy of values within the New Testament", the existing canon was maintained and none of the Reformers disagreed with the ancient views of origin and authorship of those texts. Obviously, they had no knowledge of current scholarship, but given that none of the New Testament writings mention the fall of Jerusalem in A.D. 70 (though 'Revelation' might have been written after the event) it's unlikely they would support a post 100 date.

As for whether "the activity of the Church predates the Scripture", the first century Church certainly was active even before the first part of the New Testament began to be written. The book of Acts shows that the Church exploded on to the scene, with great power, only ten days after Jesus had returned to heaven. Thousands were converted in a very short space of time, yet note how those first Christians kept quoting from the ancient Hebrew Scriptures that were their only "Bible" up until the New Testament Scriptures began to circulate and be copied. Without the ancient Hebrew Scriptures, there could be no Christianity as Jesus was the fulfilment of its prophecies about a Messiah. All the new converts in the first century were converted on the basis of understanding how Jesus fulfilled the already existing Hebrew Scriptures.

Your final query, whether the Catholic Tradition came before the Holy Writ or not - the Hebrew Scriptures came hundreds of years even before Jesus was born, so I assume you actually mean 'before the New Testament'. The Reformers regarded Scripture as the church's constitution which is (and I now quote from another history book):

...to directly counter the Roman Catholic claim that the church is the mother of Scripture. The canon, as the constitution of the church, is what constitutes a people as this people, under this government, in this body. Of course, the Reformers and their heirs never doubted that the church came before the completed canon of Scripture in history. However, they insisted that it is the word that always creates the church. ...The law and the promise were God's sacramental word (faith-creating means of grace) even before they were committed to the canon. As that word became inscripturated, the church itself found its proper constitution. ...The churches of the Reformation do not deny the ongoing authority of the church in its representative assemblies, but the key difference is this: whereas the Roman Catholic Church combines Scripture and tradition as one source of magisterial (i.e. ruling) authority, we confess that this belongs to Scripture alone, with tradition as ministerial (i.e. serving). Just as courts interpret the constitution, church courts interpret Scripture. This is why churches from the Reformation affirm the ecumenical creeds and subscribe to confessions and catechisms as communally valid interpretations of God's Word. Yet again, it must be emphasized that this authority does not arise from the church. It arises from the canon that the church seeks faithfully to interpret in dependence on the Spirit. ...The Reformers and their heirs recognized that there were many traditions in the apostolic church that were unwritten. In that era, believers were to follow the teaching and example of the apostles in both written and unwritten forms (2 Th 2:15; cf. 1Co 11:2; 2Th 3:6)... Therefore, the churches of the Reformation have received the Scriptures as the sole magisterial authority without disregarding the ministerial authority of church councils. (Pilgrim Theology pp 67-69, Michael Horton, Zondervan 2011)