[feanaro]

You're right regarding the first part, we don't have a clear explanation of how the wave function might be related to subjective experience, but that's mostly because we don't have a good account of subjective experience at all.

For the second part, there's nothing mysterious going on at all: measurement is simply physical interaction.

[kgwgk]

What are "the individual components of the wave function"? They are a mathematical construction. The wave function can be decomposed in many (and infinity of) ways. Why is one decomposition chosen and not another? Or are all the decompositions equally "(un)real"? The issue is not so simple and it's related to the "mysteriousness" of the first part.