It could be material while not being expressible by a Turing machine. If by "algorithm" you mean something that runs on a Turing machine, then human intelligence doesn't have to follow any algorithm. If you mean that human intelligence is governed by equations, then that must be true if materialism is true, because the laws of physics (or "material reality") are governed by equations.
Sure, but I don't think anyone can say with confidence "machines will never think" or similar things (unless we're debating about the definition of "thinking").
I remember reading that people who worked on "flying machines" said it wouldn't be possible to have heavier than air planes before decades or centuries (or even ever), little did they now that they already existed for a few months but the news didn't came to them yet.
