Is there a Moore's Law for Machine Intelligence?

First, you need a mathematical definition of intelligence. Leave the problem aside that you will probably not find a common definition which will be generally accepted (mostly because people have different understandings/interpretations about intelligence). It will still be very difficult to find a mathematically definition at all (which somehow matches what at least some people might consider as intelligent). And that mathematical definition of intelligence must be measurable.

Once you have sth. like this, I would like to see a graph plotting of it with some of the research results of the last 50 years or so. And then I probably can answer your question. :)

None that know of. Intelligence cannot be related to time. It is unpredictable, even a stochastic model cannot do it justice. There are too many unpredictable points.

no, progression of intelligence follows an unknown scale. it is thus impossible to say anything useful about doubling time.