Why does Jeremiah 33, Ezekiel 34, 37, Hosea 3, Isaiah 55, Psalm 89 all seem to say David is Messiah, the true shepherd and coming one, and even the pierced one of Psalm 18, Zechariah? Was David paying for his sins as Jesus, and now returns?
I don't know if others have answered this, yet, but here is one answer:
There are various kinds of messianic hopes expressed in the OT prophets, some for a "son of David" (sometimes called the "shoot" or "branch" of David; Jer 23:5-6) and sometimes for a "new David" (see Isa 11:1; Ezekiel 34, 37; Jeremiah 33, etc.) It is hard to say if the prophets expected David to rise from the dead or whether this "David" was to be a David-like king. In any case, both ideas hope for a return to the glories of the Davidic empire.
From the perspective of New Testament theology, Jesus is both a descendant of David and a new David. The NT writers view Jesus typologically as a "new Adam," a "new Moses," a "new Israel" and a "new David" since he in some sense fulfills the role of these characters and nations in the OT. He is a new Adam in that he reverses the curse that Adam brought. He is a new Moses in that he brings a new law. He is a new Israel in that he succeeds in the desert temptation where Israel failed and brings light to the Gentiles. He is the new David in that he will reign forever on David's throne. So the terminology is flexible enough to identify Jesus as both a descendant ("son") of David (and so heir to the messianic throne) and also as a "new David" who will restore the Davidic throne forever.
The biblical writers were often imaginative and bold in their use of language, and the Psalms and the oracles of Old Testament prophets are characteristically poetic in form, which means using imagery, metaphors, and generally being creative in use of language. Jeremiah 33 refers back to David as a past figure to whom God made a promise that his royal line would not perish forever, and the prophet declares that God will raise up a future king to fulfil this promise. Ezekiel 34 condemns the ruling authorities of the time and pictures God as promising to be shepherd to his people (vv. 11-22), but also speaks of David as being their prince. This likely is a vivid way of picturing something similar to Jeremiah 33. God will raise up a future king of David's line, and in this manner "David" will rule again. A similar figurative use of "David" seems to be what's given in the other references you cite (e.g., Hosea 3, etc.).
Well before Jesus, a lot of ancient Jews still hoped for a future, ideal king such as the prophets foretell, and this figure could be referred to as God's "Messiah" (= "anointed one"). Early Christians quickly saw Jesus as the fulfilment of these hopes, and so the title "Christ" (the Greek translation of "Messiah") quickly became a major title of reverence for him. But this also involved a radical new view of the nature of (or route to) this kingship . . . through the crucifixion and resurrection of Jesus.
Unless I am misreading, psalm 89 says David is the chief of the kings, God is the savior.
But in any case, the real question is: are we living in such a way that we'd even recognize the savior if s/he appeared? Let God worry about the savior, and let each of us ask ourselves if we are living a Godly (kind, generous, compassionate, not tied to money or power or fame) life.
Each of those passages was written after the death of the historic David. The prophesies were fulfilled not by the historic David, but by his descendant Jesus, "the Son of David." Jesus began the fulfillment in his own earthly life, and will bring them to completion at his return. There is no indication that Jesus is the historic David, risen from the dead.