Muscovy take approximately 35 days to hatch. 28 days is what it takes a mallard derivative egg to hatch. 'Pied' refers to the white. People who are sticklers about genetics will go so far as to say things such as 'piebald' and the like, however, unless you're geared towards the genetics aspect all of that is pretty much more information than the average duck owner needs to worry about. If a bird has color, plus white, it's a pied. So, because they have both self-blue (not the same as lilac) and white, they're self-blue pieds.
My experience has been that Muscovy begin to lay at approximately 9 months of age. That is where they will be laying approx. one egg a day. Early hatched birds will lay a few eggs that fall before winding down for winter, but won't begin to lay regularly until the following spring. I have recently heard people reporting that their birds have started laying at 6 months. Whether that is due to environmental factors, I can't say. Where I live we have 4 definite seasons, birds down south where there is 'warm' and 'hot' with a day or two of cool thrown in each year will produce an entirely different outcome.