*2a There are also higher-level properties.. *2b irreducible to and unpredictable from the lower level properties and laws...

This all this means is that, in addition to the laws which govern low-level interactions, there are different laws which govern high-level interactions. But they are still laws of physics, they just sound like "when these certain particles are arranged in this particular manner, make them behave like this, instead of how the low-level properties say they should behave". Such laws are still fundamental laws, on the lowest level of the universe. They are still a part of the code for reality.

But you are right:

unpredictable from lower level properties

Which is what I said:

That is what it means to posit reductionism; that from an information theoretical standpoint, you can make entirely accurate predictions about a system with only knowledge about its most basic [lowest] level of perspective.

Ergo, a reductionistic universe is also deterministic from a probabilistic standpoint, i.e. the lowest level properties and laws can tell you exactly what to anticipate, and with how much subjective probability.