Answer to question 1 is: half-yes, half-no. Answer to question 2 is: you need to think about dynamical behaviour, not just the states.
Decoherence does half the job of solving the measurement problem. In short, it tells you that you will not in practice be able to observe that Schroodinger's cat is in a superposition, because the phase between the two parts of the superposition would not be sufficiently stable. But the concept of decoherence does not, on its own, yield an answer to the question "how come the experimental outcome turns out to be one of A or B, not both A and B carried forward together into the future?"
The half-job that decoherence succeeds in doing is to elucidate the physical process whereby a preferred basis or pointer basis is established. As you say in the question, any given quantum state can be expressed as a superposition in some basis, but this ignores the dynamical situation that physical systems are in. In practice, when interactions with large systems are involved, states in one basis will stay still, states in another basis will evolve VERY rapidly, especially in the phase factors that appear as off-diagonal elements of density matrices. The pointer basis is the one where, if the system is in a state in that basis, then it does not have this very fast evolution.
But as I say, this observation does not in and of itself solve the measurement problem in full; it merely adds some relevant information. It is the next stage where the measurement problem really lies, and where people disagree. Some people think the pointer basis is telling us about different parts of a 'multiverse' which all should be regarded as 'real'. Other people think the pointer basis is telling us when and where it is legitimate to assert 'one thing and not both things happen'.
That's it. That's my answer to your question.
But I can't resist the lure, the sweet call of the siren, "so tell us: what is really going on in quantum measurement?" So (briefly!) here goes.
I think one cannot get a good insight into the interpretation of QM until one has got as far as the fully relativistic treatment and therefore field theory. Until you get that far you find yourself trying to interpret the 'state' of a system; but you need to get into another mindset, in which you take an interest in events, and how one event influences another. Field theory naturally invites one to a kind of 'input-output' way of thinking, where the mathematical apparatus is not trying to say everything at once, but is a way of allowing one to ask and find answers to well-posed questions. There is a distinction between maths and physical stuff. The physical things evolve from one state to another; the mathematical apparatus tells us the probabilities of the outcomes we put to it once we have specified what is the system and what is its environment. Every system has an environment and quantum physics is a language which only makes sense in the context of an environment.
In the latter approach (which I think is on the right track) the concept of 'wavefunction of the whole universe' is as empty of meaning as the concept of 'the velocity of the whole universe'. The effort to describe the parts of such a 'universal wavefunction' is a bit like describing the components of the velocity of the whole universe. In saying this I have gone beyond your question, but I hope in a useful way.