Even though I work in quantum information, this stuff is a little far from what I do (quantum optics), but I will do my best.
1. The qubits are superconducting in nature. Each qubit is a superconducting loop, in which the current can flow clockwise or anti-clockwise, which can be called 0 and 1 respectively. There is superposition possible in the direction of current flow, so you have qubits. They arrange the 1800 qubits into a lattice. There are also current carrying wires near groups of qubits, which allows them to change the state of these qubits by changing the magnetic field experienced by these qubits.
2. What they are doing is simulating some particular types of physical systems, called Ising models. These systems consist of a lattice of particles which interact with each other. If you change either the shape of the lattice or the interaction between the particles, the equilibrium state of the system changes. Usually we are interested in finding out various properties of the system when at equilibrium. Doing this usually requires simulating the Ising model in some way. Some of these Ising models - at least - can be efficiently simulated classically and these guys have tried to simulate some of these systems using their quantum simulator. They do so successfully, showing that their very complicated machine's answers agree with those of a classical computer. So they haven't shown a new phenomena or done something which hasn't been done by classical computers. They have just shown that their machine gives the right answers.
3. I am not sure where you are getting these quotes from. But its a simulation in the sense that it tells you various properties of some system. You can call simulations just a particular type of computation.
4. Their is no discussion of speed in the above, which is central to the race towards quantum computers, and for good reason. Dwave's machine is not a quantum computer i.e.\ cannot simulate BQP problems efficiently. Their machines can't address individual qubits, or do arbitrary quantum gates on these qubits, hence can't get the promised speedup of quantum computers. Therefore, they are going a different route. They essentially want to make the equivalent of Lisp machines for physical systems. Lisp machines were designed to run one language really fast. Dwave want to make these machines that can simulate some physical systems polynomially faster than classical computers.
When you see Dwave news in the future, unless you see otherwise, just assume that they have these fancy classical computers, not quantum computers and you are good.