Ayatollah So
the spoof'll set you free
It is effectively indeterministic as even with full information I cannot predict in which universe "I" will end up in. If there was a lottery powered by a quantum random number generator and I have a one in a million chance to win, the MWI says that one of the million copies of me will win, but as the measurement destroys any connections between these copies this has no impact on all the other copies that lost. The resulting ensemble of universe is deterministic, but I do not (and cannot) care for the ensemble. It is one universe I am interested in, and I do not know beforehand which one that is.
Nonsense. You know which universe: all of them. Either all the branches are you, or none are (quantum suicide excepted). You are of course free to care only for one particular resultant universe - if you don't mind being thoroughly irrational.
It might show the way how to construct a deterministic non-local interpretation of QM that would have to be quite different from Bohmian mechanics.
David Albert says that Bohm's theory is an alternative to, rather than interpretation of, QM.

Evolution does not rule out a probabilistic brain. In your example it would suffice if the probability of the brain deciding that eating those berries is a good idea was very small.
If by very small you mean less than 1 per million generations or so, then OK. I'm mystified as to why anyone would care about a probability that small.
And as for the benefits of random experimentation, pseudo-randomness will do just fine.
Instead the claim being made is as you point out "if L and p, then f", but this is contrasted with "if L and p, then maybe f", which would be the case if there is an indeterministic element in L. This is a legitimate difference between indeterministic laws and deterministic ones.
As long as you back off the claim that "only what actually happens is possible", I'm happy.
In a deterministic world, for a given set of laws and inputs, there is exactly one possible state of the world at any specific time in the future.
That's scope-ambiguous - the necessity operator could be read as applying to the whole conditional ("Necessarily, if L and p, then f"), which would make your statement true. Or it could be read as applying just to the consequent ("if L and p, then necessarily f") which is false.
The future, whatever it will be, is inevitable if we hold the laws and present state fixed.
Eh, no. The future is going to be what it will be, but that doesn't make it inevitable. That would mean there is nothing we could do to stop it. But the future depends on what we do. So it's very much evitable.