You don't need to have rooster for a hen to go broody. It's a seasonal and hormonal thing - rooster or not - they don't seem to know the difference. I have two broodies right now - and had three earlier. No rooster.
Same as you don't need a rooster to get eggs - you only need a rooster for...
I'm not sure where on the belly - but I do know a hen going broody will pluck the feathers on her chest/belly - to conduct her body heat better to the eggs.