Also, I was always wondering what is a status of Quantum Decoherence in CI? Is it accepted, rejected or simply ignored?
Decoherence is a qualitative description of a quantum mechanical process, just as is say entanglement. CI as with the other interpretations is just that, an interpretation and neither "accepts" nor "rejects" the process but rather again interprets it.
Understanding CI as interpreting the wave-function and density operator as descriptions of our knowledge about the physical system one then understands that within CI decoherence describes a particular class of evolutions of our knowledge about the system.