Almost all hypotheses have high complexity. Therefore most high-complexity hypotheses must have low probability.

(To put it differently: let p(n) be the total probability of all hypotheses with complexity n, where I assume we've defined complexity in some way that makes it always a positive integer. Then the sum of the p(n) converges, which implies that the p(n) tend to 0. So for large n the total probability of all hypotheses of complexity n must be small, never mind the probability of any particular one.)

Note: all this tells you only about what happens in the limit. It's all consistent with there being some particular high-complexity hypotheses with high probability.

There are more hypotheses with a high complexity than with a low complexity, so it is mathematically necessary to assign lower probabilities to high complexity cases than to low complexity cases (broadly speaking and in general -- obviously you can make particular exceptions) if you want your probabilities to sum to 1, because you are summing an infinite series, and to get it to come to a limit, the terms in the series must be generally decreasing.

How is it that Solomonoff Induction, and by extension Occam's Razor, is justified in the first place? Why is it that hypotheses with higher Kolmogorov complexity are less likely to be true than those with lower Kolmogorov complexity? If it is justified by that fact that it has "worked" in the past, does that not require Solomonoff induction to justify that has worked, in the sense that you need to verify that your memories are true, and thus requires circular reasoning?

With transhumanist technology, what is the probability that any human alive today will live forever, and not just thousands, or millions of years? I assume an extremely small, but non-zero, amount.

This is a well-known problem dating back to Laplace (pp 18-19 of the book).

How do we determine our "hyper-hyper-hyper-hyper-hyperpriors"? Before updating our priors however many times, is there any way to calculate the probability of something before we have any data to support any conclusion?

Nope, not yet. I have 30 years to figure out if I want to continue with cryo or if some newer technology is more worth my money.

Should people give money to beggars on the street? I heard conflicting opinions about this. Some say they just spend it on booze and cigarettes, so it would be more effective to donate that money to hostels for the homeless and similar institutions. Others say it's not a big deal and it makes them happy. What do you think?

Using Bayesian reasoning, what is the probability that the sun will rise tomorrow? If we assume that induction works, and that something happening previously, i.e. the sun rising before, increases the posterior probability that it will happen again, wouldn't we ultimately need some kind of "first hyperprior" to base our Bayesian updates on, for when we originally lack any data to conclude that the sun will rise tomorrow?

Humans underestimating the chance of being caught seems to beg the question of why they underestimate the chance of being caught in the first place. Why have humans evolved ethical inhibition, as opposed to a better sense of the likelihood of being caught? Still, evolution isn't perfect.