It's really up to the hens whether it's possible - some will go broody, some won't ever go broody. Very few will even think about going broody until it starts to warm up and brighten up a bit. Have any of your hens gone broody before? The presence of a cockerel probably makes little impact on whether they feel like hatching or not although you can encourage them by leaving a few eggs lying around and hoping they take a hint. I'm sure the cockerel will make sure the eggs are fertile, certainly in a few weeks when spring kicks in you'll see him treading as much as he can! But the big question mark is over the hens and their likelihood of wanting to sit or not - hybrid hens are far less likely to ever go broody although my MIL keeps Black Rocks and has hatched naturally and some pure breeds are renowned for being more broody than others.
If you've got hen and chicks in a run inside the main run, I don't think rats would be an issue. I've never had a problem with rats taking chicks although I know they're around - just never seen them by day and all the chickens are locked up in rat proof enclosures by night.
Like Marches Farmer says, they need different food for quite a while - first chick crumbs (I use medicated ones to help against coccidiosis when they're little) and then growers until they're POL. So you ideally need to be able to keep them separate until they're about 17 weeks - long after mum will have got bored of them - but I'm sure others don't bother.