It does predict it, this decomposition is called decoherence, where a classical state splits into a superposition of several different classical states.
No, that's not what decoherence is. Decoherence is the spread of entanglement over a very large number of untrackable degrees of freedom (usually referred to as the "environment"). This makes interference effects unobservable. But decoherence itself does not involve any "splitting"; the entanglement that decoherence spreads over a very large number of untrackable degrees of freedom has to already be there before decoherence can act on it.
And yes, spread of entanglement does mean splitting. Entangled state is not factorizable, because all states in it are split. This splitting is the result of splitting of the initial state.
No. The 100 atoms is the largest molecule that we can do experiments on without having decoherence happen and ruining our attempts to observe interference.
The number of degrees of freedom in the environment is many orders of magnitude larger, something like 10^30 or more for a typical experiment.
This is especially problematic because QM doesn't predict any particular decomposition of a quantum state into particular classical states. That is, the Schrodinger equation doesn't actually predict that a particle has some amplitude here and some other amplitude there, as is often presented; instead, it predicts that it is described by some vector which can be decomposed in many different ways. You can say it has some amplitude X here and some amplitude Y there, but with any 2 points in space-time (adjusting the amplitudes). Or, it can have some combination of position and spin with amplitude X, and some other combination of position and spin with amplitude Y. You can choose any basis you like for the measurement, and you will get the corresponding answer.
But, for MWI to actually predict experimental results (and the classical world we live in) you not only have to choose to look at a single element of that basis, but you also have to believe that the classical basis is somehow preferred.