If you are preparing for example the spin of a particle, you actually create a superposition of two states ( u and d in the respective basis vector), and when you observe it, the state will collapse to a single state, this is when you collapse the entanglement too.

Yes and no. It all depends on how large your system is, at witch you are looking at. As you said, if you look at the universe, than you get that everything is entangled, and indeed there are no product states. BUT, if you look at a much smaller system, e.g. an atom, you find that the electrons of it have very little ( almost none ) interaction with a particle 1km away from him, so the change of the state of the latter particle has no effect on our atom's state.