[lmm]

> How does nature decide which determinate state would my universe take? It still requires the magical collapse. (Or is it that I am branching off too and loosing access to myself in other branches?)

You're branching too. It remains to be explained why your subjective probabilities of which branch you find yourself in follow the Born probabilities, but that's the only known way of assigning subjective probabilities that behave as probabilities should (in terms of things like "probability of A or B <= probability of A + probability of B").

> That is, how do we know that the decision on which particle has which spin did not happen during separation itself (getting stored as a hidden variable)?

Conway's "Free Will Theorem" offers a simplified proof that this can't happen: if you measure the particle along three orthogonal axes then you will always get two of one result and one of another, but there's no way to preassign values to all possible axes such that this remains true. So the result you get from measuring in a given direction cannot be fixed if you have a free choice about which set of directions you're measuring in.