A PMC - and other similar variants of the military contractor concept - would most likely be unable to develop a WMD. Using a nuclear bomb as the example, producing the necessary amounts of enriched uranium would be a massive barrier for the company. A nuclear reactor is necessary to enrich the uranium through gaseous diffusion, laser separation, or in a gas centrifuge. The barrier arises here, as a private military organization would not have ready access to such facilities.

As for the first part of the question, I haven't been able to find any documented cases of a company owning such a weapon, however there are indeed firms which work with entities such as the Department of Defense. A lot of work in the private military field surrounds logistics and the outsourcing of work/maintenance. This could include working on such weaponry, or on installations where they are housed.

I suggest reading "Corporate Warriors: The Rise of the Privatized Military Industry" by P.W. Singer. It is a great source to gain an understanding of the private military field[s], as it provides both general overview of the types of services offered, its history, and the future of the field, and goes in-depth into examples of the types of work one could expect [and has been done] from the various types of PMFs.