What kind of jurisdiction do states have over the TSA (or federal agencies/employees in general)?

Do state speed laws apply to TSA employees driving gov't owned vehicles? What if the employee is headed to an airport for an emergency terminal dump because of a stray water bottle? How about state safety laws (e.g. zoning, construction codes, workplace safety, etc.)?

Can a TSA employee be arrested on state charges for fondling a traveler, or are they completely immune from state & local laws while on the job?