No additional classical concepts are required for a consistent quantum description
There are no particles
There are no quantum jumps
There is but ONE basic framework for all physical theories: quantum theory
There is no time at a fundamental level
Decoherence is the theory of universal entanglement. Generically, it does not describe a distortion of the system by the environment, but rather a disturbance (change of state) of the environment by the system. This may nonetheless affect the system itself because of the fundamental quantum aspect of kinematical nonlocality.
The process of decoherence is based on an arrow of time in the form of a special (ultimately cosmological) initial condition.
Decoherence can not explain quantum probabilities without (a) introducing a novel definition of observer systems in quantum mechanical terms (this is usually done tacitly in classical terms), and (b) postulating the required probability measure (according to the Hilbert space norm).