Lots of questions here. Though it does, just about, observe the Aristotelian unities of time and place (that is, the play takes place - nearly, at least - within one day and in one location), I don't think you can classify "The Tempest" as a tragedy. Nobody dies, and it ends in a marriage: which is, of course, usually seen as the definition of comedy.
But there are elements of tragedy in "The Tempest": the whole slavery question (Caliban, Ariel, and potentially even Miranda as slaves to Prospero - the argument that Prospero, usurped from Naples, usurps Caliban of his island, and so on), and - of course - the implication that Prospero will take his revenge on his brother for the way he has been treated.
That Prospero eventually forgives his brother - and tempers his desire for justice and vengeance with mercy and grace - is usually described as an entirely positive move, and, for the resolution of the play, it is. But have a look at Prospero's final epilogue: not the words of a man blessed and enlightened by his own forgiveness, but a worried, ambiguous speech that foresees an ending in despair.
Justice or forgiveness? Shakespeare leaves it very, very ambiguous.