Randomness is random, if it is somehow entangled with another system then it there are hidden variables that haven't been discovered yet. Quantum physics is "absolutely" random ( see http://en.wikipedia.org/wiki/Hidden_variable_theory for the story).
- I think the OP was referring to chaotic systems as effectively random, which they are not
- It certainly forces us to redefine what is the meaning of free will, if we dont accept dualism. Since Libet's experiments there are many others that have shown quite convincingly that our conscious "will" is predetermined from our brain processes even seconds before we are aware of our "will", and what's more that subconscious process can be manipulated. http://en.wikipedia.org/wiki/Neuroscience_of_free_will has some pointers (although i didn't read the whole)
1. Yes i should have mentioned that about the universe; the pdfs are deterministic. I dont agree about "effectively random"; chaos != randomness. But, crucially, at the level of biological molecules that mediate most brain processes, quantum effects have little significance.
3. I disagree strongly with theidea that free will can arise from quantum uncertainty or randomness. That's not free will, that's random will. Unfortunately, great scientists have like R. Penrose advocate such things, but i believe most neuroscientists believe it to be hokum nowadays.