Does quantum decoherence desctibe a deterministic universe? QM describes a system, whose state evolve unitarily, which is deterministic. The apparent non-determinism comes from the measurement problem, where the state is projected to some subspace in a probabilistic manner.
To my understanding, quantum decoherence describes the measurement as coupling the system  to a "bigger", more complicated "lab" system (more D.O.Fs?). The projection of the subsystem is determined by the state of the combined system, and is described by the combined system's unitary evolution.
Of course, for practical purposes, the measured system seems to choose its projection randomly, due to lack of information about the lab system.
Does this mean that QM is, after all, a deterministic theory with no inherent randomness?
 A: 
Does this mean that QM is, after all, a deterministic theory with no inherent randomness ?

If you could somehow work with the wave function of the entire universe then the measurement problem would go away (or at least be sidestepped) and the evolution of this hypothetical wave function would be entirely deterministic. Unfortunately we don’t know how to do that, not least because we do not have a theory of quantum gravity.
A: In quantum mechanics a system S can be in a sharp state where a measuring instrument M it you will get the same answer each time:
$$|a\rangle_S|0\rangle_M\to|a\rangle_S|a\rangle_M.$$
But S could also be in a state that is unsharp where the measuring instrument isn't in a single state:
$$\sum_b\alpha_b|b\rangle_S|0\rangle_M\to\sum_b\alpha_b|b\rangle_S|b\rangle_M.$$
It is impossible to predict what result you will get from such a measurement because there are multiple outcomes and so there is no single fact of the matter about what will happen. Rather, there are multiple versions of the measuring instrument, each of which records a different value.
Decoherence is a process that suppresses interference between components of an unsharp state. The components then evolve approximately like a collection of parallel universes.
It doesn't eliminate other components. Doing that would require changing quantum mechanics to include a process to eliminate other components. There have been suggestions on how to do that, but they all have problems like producing weird predictions in low probability branches, or adding unnecessary complications to quantum theory.
