1) The book is not a part of the Hebrew canon. It is a Greek work. None of the inspired NT authors make any allusion to this text (strange, if it was Scripture and prophetic).
2) If its literary conceits are taken at face value, this work of the 1st or 2nd century BC purports to be a Solomonic product: from ch.9
 Thou hast chosen me to be king of thy peopleThis, however, would be a blatant fiction, if it were intended to be believed on the face of it. Manifest falsehoods, however mixed with truth, make for an unreliable prophet.
and to be judge over thy sons and daughters.
 Thou hast given command to build a temple on thy holy mountain,
and an altar in the city of thy habitation,
a copy of the holy tent which thou didst prepare
from the beginning.
On the other hand, he may not have intended his work to be taken literally for Solomon's. So, these lines might simply be additional allusions to OT data which the author is gathering into a literary product that delineates his own pious and/or Messianic hopes.
3) What are we to make of the vv from ch.2, that sound so "Messianic"?
The question isn't hard to answer. The author of WoS is familiar with his Bible (OT), and in particular he is indebted to Isaiah and David for much of his language and allusions. If there be found a strong Messianic pulse in his work, then it--along with various literary remains from Qumran--proves that prior to Jesus Christ (and Christian interpretation of the OT) there was a tradition of Jewish interpretation that was able to bring together many of the strands of OT expectation, which ultimately finds "uncanny" (?!) fulfillment in the life and ministry of Jesus of Nazareth.
In other words, people like Mary or Zechariah, whose songs of praise are presented early in the NT Gospels, belonged to an established pious tradition within ancient Judaism. Their Messianic hopes were fulfilled (albeit in many unexpected ways), yea and surpassed, in Jesus. The author of this WoS is a kind of "preacher," in writing. So far as we know, he's skillfully composed a pious, OT Scripture meditation. If it puts us in mind of Christ, we still can't tell if that was the writer's intent. But it does prove that Christian reflections on the OT have what look like (or may be interpreted as) mirror images in pre-Christian Judaic literature.
I'll add, in answer to the "curiosity" of the so-called reprobate prophet, that the "clip" from the Romanist leaves off the beginning of the chapter, in which we have:
 But ungodly men by their words and deeds summoned death;etc.
considering him a friend, they pined away,
and they made a covenant with him,
because they are fit to belong to his party.
 For they reasoned unsoundly, saying to themselves,
"Short and sorrowful is our life,
and there is no remedy when a man comes to his end,
and no one has been known to return from Hades....
That is to say, the words above are put in the mouth of the wicked. This is something that the prophets frequently do, just look at David, Ps.2:3, or Solomon, Prv.1:11ff, or Isaiah, 30:16, and so on.