How do they define Qubit?
D-Wave operates based on the "adiabatic model" of quantum computation. One example of how this works, which is explained in a way simple enough that high school students would be able to understand most of it, is in this paper Quantum factorization of 56153 with only 4 qubits1. Finding $(p_1,q_1,p_2,q_2)$ that minimizes Eq. 12 is equivalent to solving the original problem (factoring the number). This is accomplished by Eq. 15.
Since $(p_1,q_1,p_2,q_2)$ are binary variables (they can only be 0 or 1), you cannot use calculus to minimize the function, and a classical computer would need to search through all $2^n$ (where here $n=4$) possible binary strings to find the string that minimizes Eq. 12. On D-Wave, each qubit represents one of these $n$ binary variables. Instead of searching through $2^n$ possible binary strings, we couple $n$ qubits together with the strengths given in Eq. 12 and find the ground state of the system.
Can these Qubits build a universal quantum computer?
D-Wave does have a prototype for a universal quantum computer, but their most famous machines which have been sold to customers have slightly less functionality in order to allow for many more qubits. They are not capable of simulating any quantum computer with at most polynomial overhead, so they are not considered "universal quantum computers". Short answer: They have the technology to make universal quantum computers with a small number of qubits, but the 2000Q is not universal.
Does the D-Wave 2000Q satisfy DiVincenzo's criteria?
Unfortunately it's not fair to ask two completely different questions in the same box, so I've created a separate question just for this part: Does the D-Wave 2000Q satisfy DiVincenzo's criteria?, and I have answered it too :)
1 Note: I'm an author