Was each "Book" of the Old Testament on a separate scroll prior to the second century A.D.?

The answer appears to be «usually» but «with some exceptions», and also «the experts aren't completely sure».

We can divide the sources adduced into indirect evidence (references to scrolls in ancient documents) and direct evidence (scrolls).

Indirect Evidence

Old Testament

The word used in the passage quoted in the question is βιβλίον.¹ While it is the most common word to designate a scroll, it is not specific to a scroll; it can label any collection of writing. In the Septuagint (Greek Old Testament), the phrase τὸ βιβλίον τοῦ νόμου (the βιβλίον of the law; translating sēper tôrāh) and τὸ βιβλίον τῆς διαθήκης (the βιβλίον of the covenant; sēper bᵉrı̂t) are common, particularly in Deuteronomy and Joshua. Here they generally seem to be abstract references to the collection of Yahweh's revelation to Moses (e.g. Deut 28:61, 29:20).

The other two clusters of usage are more concrete so perhaps more relevant: the parallel accounts of the "book" (sēper > βιβλίον) found in the temple that was the impetus for the reforms of Josiah (2 Chr 34; 2 King 22-23). This is described as a single item that is found, handed back and forth, and finally read (apparently in a single sitting). Although the precise contents of that "book" have been a matter of considerable debate, I think most scholars would identify it with Deuteronomy, or some portion thereof (Dillard), bolstering the identity between scroll and book. If one thinks the "book of the law" as the entire Pentateuch, of course, this would provide evidence for a very early compilation of multiple books on a single scroll.

New Testament

The OP brings an important piece of evidence from the NT. This description of the Isaiah scroll is emphatically concrete ("he unrolled the scroll..."). I agree with the OP's sense that this is probably a relevant reference to a single scroll containing the book of Isaiah. There are several other NT references to be dealt with in this regard:

• For it is written in the βίβλος of the Pslams (Acts 1:20, cf. Luke 20:42)

• ...as it is written in the βίβλος of the prophets (Acts 7:42, citing Amos 5)

• ...have you not read in the βίβλος of Moses in the passage about the bush, how God spoke to him...? (Mark 12:26, citing Exodus 3)

• Cursed be everyone who does not abide by all of those things written in the βιβλίον of the law (Gal 3:10, quoting LXX Deut 27:26)

Although these all connect the terminology of βίβλος with a particular book or collection thereof, they are all most likely intended abstractly, similar to those in Deuteronomy and Joshua, without a concrete referent.

Baylonian Talmud

The Babylonian Talmud (Tractate Baba Bathra, Folia 14a) mentions the "Scroll of the Law" and the "Scroll of the Prophets". In both cases, the physical characteristics are described, and it is evident that a single scroll was in view. The existence of such a scroll has been called into question (Tov, 1998), although there is no proof one way or the other.

Direct Evidence

The direct evidence must come from the only ancient scrolls we have of the Hebrew Bible: the (so-called² ) Dead Sea Scrolls (DSS). Many of these are fragmentary, but scholars have tediously pieced them together so that in most cases we know which fragments below to a single scroll. Among these estimated 210-212 biblical scrolls, there is evidence of 10 scrolls that contained more than one book of the Torah. The most substantial strictly Biblical texts mostly consist of two consecutive books (Tov, 2012):

• 4QGen-Exod^a
• 4QpaleoGen-Exod¹
• 4QExod-Lev^f
• 4QLev-Num^a
• 4QDeut^j (includes Exodus)

There is possible evidence for a complete Torah scroll (Mur 1, from Wadi Murabba'at, including Genesis-Exodus and possibly Numbers), although the extent of this scroll beyond Genesis-Exodus is a matter of debate.

In addition, there are the curious fragments of the so-called "reworked Pentateuch" (see also, Zahn). Although historically (i.e. in early years of DSS research) these were often not counted among the Biblical manuscripts, scholars more recently tend to include them despite considerable deviations from the (now) canonical text. These each contained between 2 and 5 of the Pentateuchal books apparently on a single scroll; 4QRP^c is the manuscript that contains clear evidence of all five books. The Encyclopedia of the Dead Sea Scrolls reflects on this:

It is of interest to note that our evidence indicates that, unlike the other Torah manuscripts from Qumran, in which copies of Genesis, Exodus, Leviticus, Numbers, and Deuteronomy are preserved on single scrolls, or, at most, two books to a scroll, the Reworked Pentateuch copied all five books on one scroll, which would have made a complete scroll longer (twenty-two to twenty-seven meters [seventy-two to eighty-nine feet]) than any other found at Qumran. (Crawford)

Why it is that these scrolls were constructed in such large proportions remains a mystery. It does indicate, at least, that there was no fixed limit to the length of the scroll due to physical constraints at the time the Qumran documents were composed.

Finally, we should remember that the "Book of the Twelve" (minor prophets) has been considered a single "book" in Jewish tradition for as long as we have manuscript evidence. There are (relatively) well-preserved Hebrew and Greek versions of "The Twelve" among the DSS, each a single scroll. Samuel, Kings, Chronicles, and Ezra-Nehemiah are also each a single "book" in the Jewish canon and in the available ancient evidence.

Summary

• The Biblical evidence generally points toward one book per scroll.

• The Babylonian Talmud refers to a scroll containing the entire Pentateuch, but this remains unconfirmed.

• The DSS generally include one book per scroll; there are a few that include two.

• Among the "reworked Pentateuch" manuscripts from among the DSS, at least one scroll contained the entire (reworked) Pentateuch. However, these are not strictly canonical by modern Christian standards.

_{1. Used interchangeably with βίβλος in the NT (Silva) and in this answer.}

_{2. The DSS are not all from the immediate vicinity of the Dead Sea. "Scrolls from the Judean Desert" seems to be the more accurate label, but this hasn't caught on. See the introduction to the discovery sites on the Dead Sea Scrolls Digital Library page.}

References

_{Sidnie White Crawford. "Reworked Pentateuch." Encyclopedia of the Dead Sea Scrolls (OUP, 2000).}

<sub>Raymond B. Dillard, 2 Chronicles (WBC; Zondervan, 1987), 280.

Emanuel Tov, Textual Criticism of the Hebrew Bible (3rd ed., Fortress Press, 2012), 96ff.</sub>

_{Emanuel Tov, The Dimensions of the Qumran Scrolls. Dead Sea Discoveries (1998), pp 69-91.}

_{Moises Silva, "βίβλος" in New International Dictionary of New Testament Theology and Exegesis (Zondervan, 2014).}

_{Molly M. Zahn, The Problem of Characterizing the 4QReworked Pentateuch Manuscripts: Bible, Rewritten Bible, or None of the Above? Dead Sea Discoveries (2008), pp. 315-339.}