Nuclear power plants are required to carry $200M in liability insurance, and this is provided by a joint underwriting association called the American Nuclear Insurers. It may just be a coincidence that ANI is the plural of "anus", but it gives you an idea about what it's like dealing with these guys - if they have an issue, it gets fixed (and nothing regulates a capitalist like another capitalist).
Above and beyond this, in the event of a severe nuclear accident, existing nuclear power plants' operating companies would be assessed to pay for the losses:
The Act also requires nuclear operators to participate in a secondary retrospective assessment program to meet public damages above the $200 million primary insurance limit. Any damages above a reactor’s $200 million primary insurance coverage are to be assessed equally against all operating reactors, up to a current limit of $83.9 million per reactor, per accident (a 5% surcharge may also be imposed to pay legal costs). These assessments, called “retrospective premiums,” would be paid out at a rate of $10 million per reactor, per year, until the cap is met. Retrospective premiums are adjusted for inflation every five years. The Act currently covers 106 reactors (103 of which are currently operating). As a result, the Price-Anderson Act would provide $9.09 billion in compensation in the event of a nuclear accident. Payment of any damages above this combined primary and secondary cap would require congressional action. Under the Act, only reactor owners and operators are liable for damages in the event of an accident; companies that designed reactors or provided reactor parts or construction services are exempt from liability under the Act.So nuclear operating companies have a strong incentive toward helping one another as needed to make sure that plants are operated safely, and they have formed organizations such as the Institute for Nuclear Power Operations (INPO) to spread best practices, maintenance information, parts failure info, and other common information on their own terms without recourse to govt regulators like the Nuclear Regulatory Commission (NRC).
For radwaste, operators have been contributing to the Nuclear Waste Disposal Fund for years now. These contributions come from the ratepayers as noted here:http://www.rw.doe.gov/techrep/feead_98/feead_98.htm
The U.S. Department of Energy (DOE), referred to as the Department, finds that the current 1.0 mill ($0.001) per kilowatt-hour fee charged on generators of spent nuclear fuel is adequate, and recommends that the fee not be changed.Note that this assessment dates to 1998, during the Clinton administration. The amounts are not chicken feed -we're talking around $600M per year.
Here is some more information specifically about the funding of Yucca Mountain.
As for security, the costs are borne by the utilities themselves, and violators are subject to heavy fines. It's inappropriate to go into any more detail here.
Questions? Bear in mind that I'm no longer in the industry and I have a day job and a life, so it may take some time to run things down.