1) If we ask whether the entities embedded in strings watched over by the self-consistent universe detector really have experiences, aren't we violating the anti-zombie principle?

We're not asking if they have experiences; obviously if they exist, they have experiences. Rather we're asking if their entire universe gains any magical reality-fluid from our universe simulating it (e.g., that mysterious stuff which, in our universe, manifests in proportion to the integrated squared modulus in the Born probabilities) which will then flow into any conscious agents embedded within.

Sadly, my usual toolbox for dissolving questions about consciousness does not seem to yield results on reality-fluid as yet - all thought experiments about "What if I simulate / what if I see..." either don't vary with the amount of reality-fluid, or presume that the simulating universe exists in the first place.

There are people who claim to be less confused about this than I am. They appear to me to be jumping the gun on what constitutes lack of confusion, and ought to be able to answer questions like e.g. "Would straightforwardly simulating the quantum wavefunction in sufficient detail automatically give rise to sentients experiencing outcomes in proportion to the Born probabilities, i.e., reproduce our current experience?" by something other than e.g. "But people in branches like ours will have utility functions that go by squared modulus" which I consider to be blatantly silly for reasons I may need to talk about further at some point.