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No, but it can produce something that's unpredictable from the original code. And that's spitting distance from random.

Yup, "unpredictability" or more precisely computational irreducibility is when things tend to get interesting... and this happens deterministically just fine.

In addition as soon as a system comes in contact with the real world randomness is nearly free and easy to get.

We dont know if physical randomness truly is so. It could be pseudo random with a seed (superdeterminism)

how about Conway-Kochen's Free Will Theorem? is it compatible with superdeterminism?

If you are interested in such topics, read

't Hooft, Gerard: The Cellular Automaton Interpretation of Quantum Mechanics

https://link.springer.com/book/10.1007%2F978-3-319-41285-6

Reference number 23.

Yes. Superdeterminism does away with the observer as a separate thing, so the question of free will doesn't even come up. Everything is just one evolving system.

Well, you can give it as many bits of randomness as you need as input (the tape).