Here, in my view, is one of the places where we must allow ourselves some of the conceptual play that is both the delight and temptation of theology. As it happens, the same classic doctrine provides an answer to both of our questions.
First the major problem and its remarkably available resolution. For our whole passage to make straightforward sense, the Good Shepherd must be at once God and a descendent of David. And that, of course, is exactly what classical Christology says of Jesus the Christ.
In the traditional formulation: the hypostasis of God the Son is the hypostasis also of the human Davidic Messiah, Jesus. In more contemporary language: “God the Son is Jesus the Christ” is an identity statement. By either formulation of the rule: you cannot refer to God the Son without thereby referring to the man Jesus, and you cannot refer to the man Jesus without thereby referring to God the Son.
A development of this claim within classical Christology then provides the conceptual framework within which we may understand the text’s calling a descendent of David simply “David.” In the jargon of traditional theology this development is called “the communication of attributes”: if God the Son and Jesus are the same person, then what is true of the one must somehow be true of the other, divine and human attributes must somehow be mutually “communicated.”
One of the things true of God the Son is that he transcends the divisions of time; therefore Jesus must somehow transcend them and so indeed be able to sum up in himself the whole Davidic history, appearing as himself the paradigm of Davidic rule.
One unit of the composition (34:25–29) remains before the conclusion. Here we see nature itself transformed by the rule of the eschatological Good Shepherd—shepherds, after all, live with nature. Such marvels as are here promised did not appear in Ezekiel’s day, nor were they seen as the exiles returned. If they are to happen at all, they await the day when David’s shepherding will be universal and open for all to see, so that “creation itself will be set free from its bondage to decay and will obtain the freedom of the glory of the children of God” (Rom. 8:21).
Finally the construction is rounded off and concluded by a version of Ezekiel’s regular finishing formula. Here the formula is completed by another and beautiful variant of the covenant promise: what the people will hear and learn when the Lord who is David takes over as shepherd is, “You are my sheep, the sheep of my pasture, and I am your God” (Ezek. 34:31).