The 2-periodic dg-category MF of matrix factorizations is a categorical singularity invariant, appearing on the algebro-geometric side of mirror symmetry. After recalling some categorical background, we'll explain the results in the title and how they're useful for establishing basic properties of MF and for relating its Hochschild invariants to classical linear-algebraic invariants of singularities. Finally, we'll give a description of MF in terms of "derived algebraic geometry," and see how this allows one to give conceptual proofs of the results in the title.