I didn't read all of them, but the one on determinism in classical physics seems to be mostly a straw man argument. The definition of determinism in that paper isn't one that would have used, nor is it the most common one in physics. The singularities described are ALL deterministic effects by the typical definition of determinism. Now, the examples *do* show some of the problems inherent in the specific classical laws described. In particular, situations where particles go off to infinity in a finite time are inherently problematic. But they are still quite deterministic. And, they cannot be 'run backwards' and get valid solutions, as claimed.
The lack of determinism in quantum thoery is of a much different character than these examples. For one, QM is not a realist theory, nor is it causal. Both are relevant to determinism.
First, the lack of causality is pretty directly related to non-determinism: that several different results are possible from a given initial condition is *precisely* the lack of determinism. So, even though the evolution of the wave function is deterministic, the actual physical results are only probabilistic once the wave function is known. And the wave function is taken to be *all* that is knowable about a physical situation.
Related to this is the lack of realism. In QM, things do NOT have definite properties at all times. In fact, any non-stationary state is going to be a superposition of more than one state with definite energy. That means, already, that the energy of such a state is not definite. But the same can be said for almost all observables: most real states are superpositions of eigenstates and so do not have definite values for the observable.