Q: So does the non-existence of randomness also imply the non-existence
of free will? (*)
To avoid more misreadings, some definitions:
Randomness means lack of pattern or predictability in events. (Wikipedia)
[..] we shall define determinism as the metaphysical thesis that the facts of the past, in conjunction with the laws of nature, entail every truth about the future. (Stanford Encyclopedia of Philosophy)
I equate a world without randomness as a fully predictable world, thus a deterministic world.
Note that our world seems to be somehing in between, e.g. the solution of the Schrödinger equation of an electron of a hydrogen atom gives a probability distribution of its positions. It is neither fully random, because the electron will over time be found at positions in accordance with expected probabities, they form patterns. Nor is it fully deterministic, because we have no means to predict the future positions from the past information.
So the answer to your question (*) is:
A: If the additional condition holds that will is determined by the
world then if the world is deterministic then the will, which is
determined by the deterministic world, is deterministic as well. Then
there is no free will.
Initial states and time propagation laws would determine the future states including the states of mind.
Important here is the relationship between mind and the physical world, e.g. see the :
The mind–body problem in philosophy examines the relationship between
mind and matter [..]
A variety of approaches have been proposed. Most are
either dualist or monist. Dualism maintains a rigid distinction
between the realms of mind and matter. Monism maintains that there is
only one unifying reality, substance or essence in terms of which
everything can be explained. Wikipedia
Example: The functionality of a computer program is based on physical state, esp. the contents of its main memory, state in the processors and hardware devices. We can save that state and at a later time reload it and have the system continuing exactly from save time. (This is commonplace today in guise of a sleep function or in virtualization software)
If we had a device that would be able to record all matter within a certain volume and its state and then at another position and/or later in time be able to recreate all matter and enforce the recorded state, we would expect a working copy of the computer at the second location and or second time.
However if one would use the same device on a living being or a human, the result could be interesting, depending on life and the mind to be completely described by the matter in the volume and its state. In both cases we do not know if that would suffice. Or maybe the mind is a non-local phenomenon, then the limited recording volume could be cause of not getting a pefect copy.
Q: Wouldn't this imply that all events to take place in the future are
also predetermined and can be calculated? (**)
Taking the above described position this would yield the answer:
A: Having the full knowledge of initial states and laws, one could
calculate the future states.
Could we do this? Most likely not, because we are living in a world which seems not fully deterministic, we have only finite resources and time (both limiting our computational power) and have no full knowledge of the initial states and laws.