No. The PeaCOCK is the male of the species of bird called PEAFOWL. Not surprisingly, it is the female of the species, PeaHEN, which lays the eggs. The eggs are a bit bigger in size than a chicken's egg.
None. A peacock is a male bird, so it cannot lay eggs. The female equivalent, peahen, lays the eggs. On average, a peahen lays a single clutch of eggs consisting of 4-8 eggs, once a year.