Mechanics is not a physics term in the first place, but a logic term. It means "natural link of cause and consequence". When something happens, it has consequences, and the sum of both a cause and its consequence is known as a mechanical phenomenon. So, the knowledge or study of the intimate behavior of something is known as the "mechanics" of said something.
Quantum Mechanics is the branch of Physics that studies the intimate behavior of the particles and phenomenons of quantic scale.
If by "the laws of physics" you mean to include quantum mechanics, then yes. If you mean purely Newtonian physics, then they imply the exact opposite.
Principles of Quantum Mechanics was created in 1930.
The distinction is sometimes made to distinguish normal quantum mechanics (which does not incorporate special relativity) and quantum field theory (relativistic quantum mechanics). Since we know special relativity is correct it is the relativistic form of quantum mechanics which is true, but non-relativistic quantum mechanics is still used, because it is a good approximation at low energies and it is much simpler. Physics students typically study regular quantum mechanics before moving on to quantum field theory.
Ordinary matter is anything that has mass and volume, but the ever advancing field of quantum mechanics is changing this definition.
The concepts of quantum mechanics were not explored until the 20th century. Newton only lived into the 18th century, so Newton did no work on quantum mechanics.
The mixed state in quantum mechanics is the statistical ensemble of the pure states.
Quantum Mechanics "replaced" Classical Mechanics in particle physics in mid-1930s.
It is also called wave mechanics because quantum mechanics governed by Schrodinger's wave equation in it's wave-formulation.
Classical Mechanics and Wave Theory.
Quantum mechanics is a separate branch of physics. It is a general term given to all quantum physics. There are many subbranches, for example Quantum chronodynamics which describes the strong nuclear interaction.
There is no reasonable alternative to quantum mechanics, at least not something that can even compare with the predictive power and experimental accuracy as quantum theory. If you want to make predictions about things happening at small scales you cannot do without quantum mechanics. Also note that certain models which are now considered as possible theories of everything (e.g. string theory) all expand upon quantum mechanics, they do not make quantum mechanics invalid or unnecessary.
I am not aware of it "not being explained". I would guess that you can explain the relevant aspects with quantum mechanics.