It varies but usually about 18 months for the first full molt. But it's usually in the fall so it could be much earlier. I have a flock hatched in march that almost all molted this year starting at about 8 months.
Provide your birds with gamebird feed, it has higher protein content than layer feed. That should stop the picking/pecking. Rooster Booster 'Black Salve' is better than the 'no pick.' I've used the 'no pick' and my birds gobbled it up like it was a treat. They didnt mess with the 'black salve,' it also contains healing ingredients. Vicks Vapor Rub should deter picking/pecking as well, cheaper too.