I've only done first year Uni Physics, but i have considered this very problem at great length, here are my thoughts:
From a classical physics perspective, the universe is 100% deterministic. Thus your second assumption would be correct.
However, Classical physics is incomplete. Currently the greatest theory for understanding modern physics is taken to be quantum physics. Now I am not necessarrily saying that quantum physics is complete or perhaps even correct either, but at this point it is the best thing we have.
Now: in quantum theory, all particles are waves, and (I won't bore you with the details) due to this, it is impossible to know with 100% certainty both the location and the velocity of any particle (look up Heisenberg's uncertainty principle).
Now one could argue that it does not matter if we know both, all that matters is that they have both. The theory seems to imply that it does not actually have both unless measured which would render such an argument moot, but as previously, quantum theory is not perfect.
3. Assuming that all particles DO have both a certain location and a certain velocity at any certain time, then yes, I agree the brain could also be predicted. If not, they it cannot be predicted with 100% accuracy. (Though since our brains do not manipulate the quantum effects, and thus cannot control the randomness, they still probably are unable to actually exercise free will.)
Personally I think that it makes total sense that we can never know anything to 100% certainty, once you do alot of physics this much becomes apparent.
However, i do not believe that the fact that I know something is necessary for it to have happened or exist, thus I do believe that it is deterministic.
This has led me to 3 important realisations:
1:
If we accept the possibility that a 'God' exists, then its interaction with this universe is dependant upon this argument!
If everything is deterministic, then the ONLY possible time that god MIGHT have interacted with the universe is at its very beginning. This means that it doesn't matter what you pray to god for coz he cant do a damn thing more!
Alternatively, there does exist true randomness, and this presents an opportunity for 'god' to interact with the universe subtly by ensuring that certain 'random' events turn out the way it wants.
2:
I had once used your argument that it was possible to predict the future by knowing the conditions at any one time and having a perfect understanding of physics. I also knew that all possible variables must be calculated, thus the only way to predict with 100% certainty was to simulate the entire universe.
I imagined that a supercomputer of infinite power could simulate the entire universe in fast forward until it was viewing the future.
Unfortunately this hit a dead end when I realised that the computer would be required to simulate itself simulating itself simulating itself etc etc since it is a part of this universe, thus no matter how powerful the computer, you cannot possibly predict the future with 100% certainty even if you know exactly what the universe was like at one given point in time.
3:
Less importantly, if the universe is deterministic, then there is only one possible way in which events can occur, thus there is no multiverse.
Anyways, philosophical or metaphysical food for thought =P